数学建模社区-数学中国

标题: 311数学结构种Mathematical Structures [打印本页]
作者: lilianjie    时间: 2012-1-12 13:19
标题: 311数学结构种Mathematical Structures
9 G  E" ~" Z. X6 ^9 H
# t) e8 A- H; j  @9 l4 V8 K
Abelian groups     Abelian group5 G0 G7 W3 `2 R+ o
Abelian lattice-ordered groups
  ~/ M  F. S# N4 v! eAbelian ordered groups$ w% R9 N, t1 v  r, Z
Abelian p-groups
! J7 J& n5 C% l* [& W6 SAbelian partially ordered groups; X: C! F% H7 e/ i/ P5 k2 g  D
Action algebras     Action algebra
9 |+ T! D; w9 V) g1 G0 s, O8 jAction lattices; N9 \6 K0 e; R. R' q
Algebraic lattices$ J" J  c; z# J0 a
Algebraic posets     Algebraic poset; q% r1 z) [4 r4 x6 ?$ V8 p# q
Algebraic semilattices
% I( |2 ~+ i. y2 E0 gAllegories     Allegory (category theory)
* P3 y( t  i# i( T9 d5 h/ IAlmost distributive lattices/ @1 y! A4 d4 B8 q
Associative algebras     Associative algebra
) W/ @* r. T$ }7 I: SBanach spaces     Banach space8 T. p5 }& ~1 i- @+ ^
Bands     Band (mathematics), Finite bands
8 ~5 r& @7 {0 n; LBasic logic algebras
8 y, K* x! m  Q. ]  V- H$ jBCI-algebras     BCI algebra' o; K+ }+ x9 Q$ Y7 b" X! P
BCK-algebras     BCK algebra
1 O# R2 t  H; r. W! g" [" j* @; dBCK-join-semilattices5 @8 t! y! O$ Z9 O: D2 `! o9 e
BCK-lattices
# u1 ]* P% c* g+ BBCK-meet-semilattices
( p4 B& H; R; C# [. iBilinear algebras
: T" Z8 q. e  s2 d6 HBL-algebras
" O% o! W. @5 L3 F+ K0 V) S$ oBinars, Finite binars, with identity, with zero, with identity and zero,
4 ]% ]; K0 H, k8 _' c3 ~+ F6 T& ?Boolean algebras     Boolean algebra (structure)
2 O$ P2 B3 F4 CBoolean algebras with operators
. y# A  E/ l: {6 ^/ q/ EBoolean groups9 b1 f' F1 A; w% |* R2 ?. Z. @
Boolean lattices0 d0 q' L0 Z9 a5 ?9 H) w
Boolean modules over a relation algebra
) A- k8 S6 |& F) [# p+ t8 @$ i3 V$ DBoolean monoids
# `' p5 m8 h5 y7 a( m6 jBoolean rings! t3 z3 M2 }. o2 _7 g
Boolean semigroups
+ ^0 Q" M# i! b+ ~' ~. D8 `- d8 [& CBoolean semilattices
' H( R, q$ o/ }Boolean spaces
- I. K4 a+ S0 }+ N: Q+ X4 {Bounded distributive lattices
. R* H6 L7 b9 p( o( `% kBounded lattices4 H# V% ^& K) `
Bounded residuated lattices
4 ?( r$ u- ]9 t& |6 I7 mBrouwerian algebras* P* [+ u, n& Y5 _* T
Brouwerian semilattices1 K: @. x' ]% P( k6 |8 S* l
C*-algebras* n, ]3 {6 M2 N- x
Cancellative commutative monoids2 d; m1 o! Y! q9 E6 v5 Y
Cancellative commutative semigroups
6 M- d. W- R, x1 A5 D. `# aCancellative monoids9 |( j$ a. c% u8 S
Cancellative semigroups5 L3 U/ k! W- M8 k
Cancellative residuated lattices% K: T! y+ \! @& D& ~9 S
Categories
: t$ p# S6 \( J2 cChains
' J( [; c2 |/ D' r) C3 R9 f( AClifford semigroups
2 P. s+ t( r& TClifford algebras
: B  Q8 z4 }% }3 Q! T& H0 p# P6 aClosure algebras
' b  ]& Q9 K4 _* h! S7 r3 [Commutative BCK-algebras) M" p3 d! g1 T8 N2 F: A
Commutative binars, Finite commutative binars, with identity, with zero, with identity and zero ( {/ T# r2 R, l; ^- b3 {
commutative integral ordered monoids, finite commutative integral ordered monoids  r! B# Z) e9 X( b4 ^8 }( X
Commutative inverse semigroups
+ I& ^- ^6 K+ MCommutative lattice-ordered monoids# n7 Z% O( z8 d( Z
Commutative lattice-ordered rings& t: U* D1 i" C; d9 V0 A9 s- m( j( R' V
Commutative lattice-ordered semigroups
; `% t0 V8 M. [8 I2 a. bCommutative monoids, Finite commutative monoids, Finite commutative monoids with zero7 h6 B" j9 l. R9 m# a( y! Q
Commutative ordered monoids
& T/ o/ a- A! r% V* H2 k1 W; qCommutative ordered rings( m& `' d9 Q! C5 H& |
Commutative ordered semigroups, Finite commutative ordered semigroups
; S" d! ^# f# K9 ~- T$ tCommutative partially ordered monoids2 V7 ~( G: b/ j, y
Commutative partially ordered semigroups
( d: L& U- B3 B( tCommutative regular rings
" W2 D. ~- ^$ r% o2 h8 [) v9 cCommutative residuated lattice-ordered semigroups. F) S0 Y  m, ]- V
Commutative residuated lattices( b- O0 a- |# V) f8 p# u7 R
Commutative residuated partially ordered monoids
9 ^  M5 v3 b3 `$ uCommutative residuated partially ordered semigroups
, M2 D% \9 C8 ~0 ICommutative rings7 J" C: B; [+ |. P0 V$ u# \
Commutative rings with identity# J- P. G  ?$ S4 S
Commutative semigroups, Finite commutative semigroups, with zero
# |/ o) J9 m2 I* vCompact topological spaces
/ u  o8 [+ _8 U" K7 _2 |8 {# @Compact zero-dimensional Hausdorff spaces
2 d* f( |$ j, m6 }Complemented lattices
0 e/ f* T% o7 \8 WComplemented distributive lattices
; g6 @9 E, t7 Z7 m5 r3 mComplemented modular lattices
. V# _/ z: x: k3 I+ _  HComplete distributive lattices
7 C, h4 i. l( U% I$ X4 M; iComplete lattices8 h( z) r1 Q: ]3 x" Q' d9 B$ k. i+ \
Complete semilattices
0 c+ }3 ?1 e" N$ J1 H, kComplete partial orders0 T; M/ c* ]1 a% @7 }/ n
Completely regular Hausdorff spaces
; B8 S3 Q/ d1 S* u* s1 DCompletely regular semigroups
4 ?" \; m$ [" g3 n! ^0 @" G* JContinuous lattices" R2 Y% }  E3 H: F0 B
Continuous posets
% D1 t: [  p& n8 I2 }3 `( N; j6 a# }Cylindric algebras
* p* x/ E0 }3 w, i2 L- p. z7 yDe Morgan algebras
5 p8 X$ |2 j" U% W& dDe Morgan monoids1 c2 ^. g3 Z& D+ B3 D" ?
Dedekind categories
4 a3 M: V3 t, ZDedekind domains
3 O1 ]+ K$ ]" j1 {Dense linear orders
; q6 H) F" U' |( X8 U# fDigraph algebras! i5 e" A6 C5 @/ h8 k3 Z* }
Directed complete partial orders& d0 O/ R4 `# r! O( A/ q" {2 {
Directed partial orders8 A) K& v3 _2 G0 t1 |
Directed graphs. ?( Z" |  H1 j, Y" D. h
Directoids6 j2 t) z8 c- ]2 ]3 E2 M
Distributive allegories+ q9 ?8 |9 F4 h- y2 q/ v
Distributive double p-algebras* @& S3 V+ t8 q
Distributive dual p-algebras" }6 T; S) k8 H4 t( d: q# a7 o
Distributive lattice expansions
. H" X3 c2 I8 D0 YDistributive lattices
7 Q; Q+ V" O$ v: D5 }' ^  w7 s# dDistributive lattices with operators# \+ U# V3 L8 n, [. B- w
Distributive lattice ordered semigroups- C# D% B" c3 }. z! I, x4 b
Distributive p-algebras
% z8 E% q* u% l' G6 N5 IDistributive residuated lattices; I3 u1 H8 @# ]& o
Division algebras- T/ i" t+ O  Z% q2 j) ]8 `
Division rings0 z/ D; l# R% W/ w, ^; o3 _* g8 ?
Double Stone algebras8 B9 k. ~- T" a5 t0 \
Dunn monoids
! q: Q& D6 X- Q4 s( P3 gDynamic algebras
0 n8 Y( q1 d5 S. V' f% FEntropic groupoids3 J, X- [3 U2 ^) h' ?
Equivalence algebras
& o7 N3 S; g+ f, u6 M( BEquivalence relations( ?1 V1 v: u' I, [
Euclidean domains
2 O- C9 @% ]" V) @) T( B7 W9 hf-rings; }& m+ e: X, C/ v4 {5 U6 F! f
Fields& z8 V3 ~% E  S: J# K' `2 u
FL-algebras: I$ o. F/ G6 ~2 Q
FLc-algebras% g# F% f) s9 S4 H$ A" o' u% E. P
FLe-algebras
' z" u! _: V; Q2 v  G7 {" M+ uFLew-algebras
& ?, z4 {$ `6 E4 ^; e" {FLw-algebras
8 E7 N& e# ~* ~: E# e! c- y( T2 zFrames" r1 f6 L, ^2 u& t" }) n: d) n
Function rings
+ r: G* o" X' o; i+ S6 LG-sets$ `8 f  P9 T" ~
Generalized BL-algebras
% l% n7 n- u) y& _* IGeneralized Boolean algebras3 Q# P4 v5 ^: \, d
Generalized MV-algebras, i& |, B9 Z( e( E1 b
Goedel algebras7 g, t  J! n9 b* o8 l# c- f
Graphs( D$ Z6 y! U7 n1 z! d* ?
Groupoids: [* o( _( o$ |) F/ {) t& `
Groups' f; X( Y2 W7 j$ g6 Y. s
Hausdorff spaces
, O+ [/ S; u/ T2 THeyting algebras
2 b" W# P( D2 e. dHilbert algebras. o  P$ X$ L! @, L" D# U. ?
Hilbert spaces$ I: {0 c0 l, R: q
Hoops
, l6 |3 {. z5 T$ `4 \Idempotent semirings
6 p: w9 V* T* A/ T+ d. t' JIdempotent semirings with identity
( w( d" o1 _- E0 |! ZIdempotent semirings with identity and zero
, l& v7 `) x# ~% jIdempotent semirings with zero
( T) G! N) K: ~- p' S& D/ ~1 wImplication algebras" k- ^* C! O2 L) x
Implicative lattices
0 @5 a. K0 v4 n3 _# X4 L2 `Integral domains
& ^1 b6 `1 z7 c% L0 O8 [Integral ordered monoids, finite integral ordered monoids
. \& T2 e. t1 b8 _9 X% R0 kIntegral relation algebras( O: M; e$ \! y. [
Integral residuated lattices
# B: v3 i$ C6 X1 eIntuitionistic linear logic algebras, j0 a8 F8 v, G
Inverse semigroups' f) O* N" r1 {" f$ \% }5 t
Involutive lattices
9 z. V7 w  i& ~; }Involutive residuated lattices
" N. W6 n, b# I" j5 P3 c  Z8 EJoin-semidistributive lattices/ A! N: ^6 D( O/ a& I
Join-semilattices% _: R! P& X. s
Jordan algebras
# }# y( X- E9 O2 B" s) K) tKleene algebras6 M  \% X& e6 E9 Y! {
Kleene lattices
6 Z  V9 @% O- E6 YLambek algebras
+ f. `% F6 _) A  N7 V' i% U5 ?Lattice-ordered groups" f6 o, u/ Y3 X& ^) ?, ^
Lattice-ordered monoids
# K3 x8 i. Y. `$ g3 S7 o+ MLattice-ordered rings
7 k1 D: W/ ~& S# R4 o2 J/ lLattice-ordered semigroups
& q2 \! N; r6 f* D# q% y9 [8 LLattices- B  P- R% R9 V# p6 U
Left cancellative semigroups; i0 ^9 L: F9 I5 `# Y3 i, ~8 C
Lie algebras
2 n6 R+ W: D- Y6 k% \* D' fLinear Heyting algebras! H# Z4 y, W( ]$ s/ t
Linear logic algebras
1 U1 ]& d8 @! k4 @* GLinear orders
" m; _8 k- t; t+ GLocales3 [6 {& T5 \4 Z1 _, k7 K
Locally compact topological spaces9 j8 T; e7 r; b2 s
Loops
9 R1 O' J* j- z/ J: N3 G# Q' nLukasiewicz algebras of order n2 B+ V9 A' A1 z) S6 v( B3 U
M-sets
- k" g& a' e# i: r9 S9 XMedial groupoids" B. V* G0 u2 l' R
Medial quasigroups% V4 t; x- q7 o' [
Meet-semidistributive lattices5 A& X7 s( f  W7 V9 q) m( g
Meet-semilattices
' _0 b( k; W% O2 q1 H8 AMetric spaces
, \1 J5 m( B! B) d! ]8 hModal algebras
1 F! }$ v2 k& x! T" K) VModular lattices6 i- n0 ]  v, g+ }
Modular ortholattices, ]4 u- {; X, b, J9 g$ q* q
Modules over a ring; N, b' V4 }. v" T2 \0 Y- S# V
Monadic algebras) c+ _7 p9 t0 \$ D/ |
Monoidal t-norm logic algebras: V8 |- O5 F$ h; _/ W+ g
Monoids, Finite monoids, with zero- R0 o1 S" v: s* i- W
Moufang loops
% ]9 S: g' W7 u* O3 ^1 @3 X9 QMoufang quasigroups
# F7 w. B. Z" C9 t7 AMultiplicative additive linear logic algebras
  v0 A9 z3 j/ e& bMultiplicative lattices
" |; K! V7 _# Z4 A0 _  IMultiplicative semilattices# K$ M- E& k2 L( _1 M; D! r& q
Multisets
& p. S) v* v& K/ FMV-algebras2 z* g8 e( Y6 v  N; H
Neardistributive lattices
+ {# A" T! Q6 K2 d' ^0 m7 E- D2 C6 SNear-rings$ h6 @, w2 I. a0 p- H
Near-rings with identity
0 }# O8 x" B- _+ CNear-fields2 a" f/ n! |! ]# [! q9 G5 S9 P
Nilpotent groups
0 W4 C! k3 W5 I0 u* YNonassociative relation algebras
7 [( @0 G7 ~7 Y8 tNonassociative algebras; v9 p* Q& P$ g3 x* Z3 Y
Normal bands
% P( {; ^' b( O! JNormal valued lattice-ordered groups' m8 k3 k9 R9 p' q  J
Normed vector spaces
2 ~+ s) R1 T2 x4 ]7 N- Y& \Ockham algebras" q' b: M6 Y* {2 u. }( S
Order algebras- y- T: C! g3 C3 ?8 M
Ordered abelian groups
# X$ A( z1 f$ m+ H: K# ROrdered fields
% u. q9 i1 u, L9 BOrdered groups0 U4 |' p/ c1 A$ e1 k2 L4 M& q
Ordered monoids
7 L, J; N0 b9 f8 VOrdered monoids with zero3 w% v. b# {8 p' j' z5 Y
Ordered rings% l, `5 Z0 g/ K3 z8 b8 T( [
Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero" R+ h  i7 d6 O; R
Ordered semilattices, Finite ordered semilattices
- a1 d/ A5 d: }( m7 o0 T& H/ ]Ordered sets
# j4 ]" X& A7 h3 g0 ~" YOre domains2 x; R( D3 |0 r- p
Ortholattices" J7 f8 M( z; J8 r( u
Orthomodular lattices
1 R) H. R& I; }" m4 P4 N9 Sp-groups
( }) @! h" x. |  W" q1 i! S  qPartial groupoids' w6 r  ?( d0 s( {6 ^# V' U9 r0 d
Partial semigroups
9 K9 o7 X) @/ z) h$ r5 K1 aPartially ordered groups6 B8 [9 }' p% e9 L! k
Partially ordered monoids
( W) H1 u0 `- E1 ~3 TPartially ordered semigroups
/ p4 {8 G3 w* hPartially ordered sets9 d. U' G. W& o/ s) z& W
Peirce algebras) ?0 e: O5 e2 B6 ]7 A' P% U: n
Pocrims7 R" v( a- f( J9 i9 e
Pointed residuated lattices
) n3 _6 j; T0 C2 p5 LPolrims  b# D! L, D. T& ]0 e
Polyadic algebras
9 n7 L3 _( l8 q; S) gPosets9 R% A) Q# c/ c! Y' k8 ^3 Y
Post algebras
8 O5 \* a# k7 S6 \7 j6 MPreordered sets6 K# l) {! r/ W  |! |
Priestley spaces4 Q; ?+ Z, o0 _! `: Y
Principal Ideal Domains. Y$ P5 \1 i; D; J; y7 G' \! x. h
Process algebras
3 i6 J. G0 {. ]Pseudo basic logic algebras
. k* r: t% \6 f( L4 Z8 s+ NPseudo MTL-algebras  g# n, S( K3 l' [- {) ?
Pseudo MV-algebras
7 I6 Q5 y/ |1 Z8 Z* }& _4 z$ pPseudocomplemented distributive lattices- }2 Z; I0 h: Q( {+ @8 K
Pure discriminator algebras9 c# |% l1 H* Z  g3 N" L
Quantales
; C3 D  a9 Z: r5 l# L. S: YQuasigroups$ }5 T% [& T9 r0 S! D2 w
Quasi-implication algebras- N+ t% G  Q0 s9 ?
Quasi-MV-algebra
4 K7 \7 k, j0 c" H8 ^; tQuasi-ordered sets
0 i1 h+ @5 Q; n3 HQuasitrivial groupoids  b6 V0 |3 l2 {! o1 E
Rectangular bands* x. j; m. E+ F
Reflexive relations4 c' J& n* B8 @$ x# J4 V" _# T
Regular rings
5 z3 a; J7 @7 F' t- b+ URegular semigroups3 Q& m$ k, l! J5 |. {9 g1 r
Relation algebras/ @( G8 h  S" r2 T, Q* Z
Relative Stone algebras
4 F" _9 o- E" G: q$ [- |  E$ A. _Relativized relation algebras
1 B3 K8 [4 t# \& [/ vRepresentable cylindric algebras- f* l2 l: {+ B' [1 V- ?7 o/ w
Representable lattice-ordered groups% ~8 w6 O1 a) C. j8 f
Representable relation algebras2 Z7 W& ~8 [5 t. B" F) n. z# Z
Representable residuated lattices
! |8 s" ^# [/ d9 jResiduated idempotent semirings
0 ?" S) n5 ?. W( q& u# sResiduated lattice-ordered semigroups: R  T+ D, O! T2 T& K  ?- ]1 H- Z
Residuated lattices
- S4 T: i6 z* \. V! tResiduated partially ordered monoids3 J: b2 p8 Y' q  C9 O# ~; X+ B8 k# L
Residuated partially ordered semigroups
2 b2 `, |- n% N% V# b% sRings
4 Z- Y& a3 i. _: G" xRings with identity) R( a$ `6 j/ G; r9 z0 K' l& U* N- {
Schroeder categories
% ]- K2 m* Q! O* ^Semiassociative relation algebras
# E& x+ M2 \# `9 E! Y4 h/ T; ]2 BSemidistributive lattices
! F5 ^2 ]2 w9 \2 d9 n2 [% {Semigroups, Finite semigroups8 i; Z" [2 F0 A% P. d3 @
Semigroups with identity
- m, K5 ^% I7 e/ l  o0 bSemigroups with zero, Finite semigroups with zero
" }. \2 a" B2 G9 e' t( RSemilattices, Finite semilattices
- {6 l& f  O1 vSemilattices with identity, Finite semilattices with identity3 a2 ?, m# N2 P4 S0 E3 b5 C# A6 n
Semilattices with zero3 _( S, [: r! T; O+ q6 i
Semirings1 r6 N  `8 q2 M  N+ p4 S+ P* _/ N
Semirings with identity4 Y! P4 n6 m, D# m- a- f
Semirings with identity and zero
  g/ ^& s% |: P6 {6 J1 lSemirings with zero/ n) s+ @$ b- W+ b5 ]2 m) x- D* L1 E
Sequential algebras  H$ Y$ A* ]# O7 o6 v+ @
Sets+ B- e  b: U+ c2 ^0 J/ {; ?
Shells/ H' D3 C  n- D  H+ [  `3 `3 e  y
Skew-fields7 G6 f4 ]* l8 \; b
Skew_lattices
2 W; @$ p+ ]0 E6 a/ Y" nSmall categories# t2 Z; E' k) G2 l& F$ X5 w# s* T
Sober T0-spaces
# d; x( I2 ~: J4 MSolvable groups0 u! v, v+ G  `& F8 R1 m
Sqrt-quasi-MV-algebras
( \" B4 ]) I4 g- e. _Stably compact spaces$ z6 S$ e6 [6 O7 m9 W3 k
Steiner quasigroups
& C4 p1 P$ ~: S1 `& m  DStone algebras2 k% c2 d$ X# {5 o- n
Symmetric relations
8 A5 o2 ~9 \3 k* `& F/ ~8 gT0-spaces
$ P* e1 g) k' }1 }+ e& |- S) nT1-spaces( c1 l0 n' o0 |% z3 `6 Q; }
T2-spaces
1 Y+ o2 X% i/ b% }0 g% j( }6 \Tarski algebras  t: h7 r$ f! j* o7 M. j8 J) P
Tense algebras
% y* P6 v! ?! J9 |5 e9 bTemporal algebras$ S4 m; e3 W; |& S) P
Topological groups3 A* Z' k/ w# W3 s& X
Topological spaces
5 j* Z( b0 ?. @3 P7 A( yTopological vector spaces
0 f1 p  B- `& Q( E" C* E7 NTorsion groups
/ _% U  A/ {" U. u* l7 A0 s9 tTotally ordered abelian groups& C+ K% d8 v( X( C: v6 K
Totally ordered groups- A+ j$ J0 T5 `( I- A1 W; x4 D7 u! z
Totally ordered monoids
# n5 W/ \9 k$ ]Transitive relations# a% K1 g* F* q1 R7 F
Trees
; |+ ~: v( M5 w( M/ r, ETournaments
* x9 R. \3 r8 G- M. G  gUnary algebras
! b7 {+ y: @5 l+ IUnique factorization domains% k8 j0 A, P% l  T5 t* K$ j- M
Unital rings6 y1 i8 ?( [! w- Q. W1 d1 O
Vector spaces
# F" ]- `+ v. P8 \# P7 S0 ~( QWajsberg algebras6 E" F: H, m* I0 \. \7 B
Wajsberg hoops
8 f+ f4 ]6 z; p; h: TWeakly associative lattices- N# p! c7 ?8 o7 c1 C# H
Weakly associative relation algebras
# H# R3 N  `# ^' D5 tWeakly representable relation algebras
- y  E' F- E0 D7 U9 @2 g7 L
作者: lilianjie    时间: 2012-1-12 13:20
阿贝尔群Abel群
8 u" @( Y" C0 {& R阿贝尔格序群& U) x& P7 p* [
阿贝尔下令组  P/ q7 S0 K4 V! T3 I
阿贝尔p -群4 {1 _+ p6 r2 r; i4 a: x
阿贝尔部分下令组. ^& P% K1 C0 p5 h
行动代数行动代数- ^4 j4 n2 X! z' S5 G. u8 j
行动晶格
0 T# J. l! z8 \1 H代数晶格
( w( O5 T6 [! c代数偏序代数偏序集2 b* m  @2 Y3 s4 [! N' q
代数半格9 u" p. u8 E" G, n! f, ], H- e9 r
寓言的寓言（范畴论）
1 q/ f0 ?+ V5 P3 {几乎分配格
. T8 W, k  F# ~, f9 J. M& B  K关联代数关联代数  ^- [. s2 d0 i9 V
Banach空间的Banach空间
% m) n: t: \+ {- z! U乐队乐队（数学），有限频带
8 R& d/ i. T: _! ~$ N基本逻辑代数
/ I) }. d) Q$ bBCI -代数的BCI代数* h8 A, w2 ~+ A' ^
BCK -代数BCK代数5 }; x1 H& s1 Y7 A" c7 `
BCK联接，半格3 q  D1 m; G1 \# H0 |
BCK晶格
9 l+ }' ?2 Z# {6 O: S* uBCK -满足的半格1 ^9 x9 f, w% `3 X4 C5 A; b* w
双线性代数) O- s  j# m1 U! O" J6 n: l& B1 d
BL -代数" ]9 s( q/ j8 P' G% O
Binars，有限的binars，与身份，身份和零与零，
8 Q" L" Y: y/ a; i, }; l布尔代数布尔代数（结构）2 I6 k) @. n, }
与运营商布尔代数
- t7 b* j# y- y& j9 U布尔组+ K7 b- I( u$ o/ Q
布尔晶格6 f: O( p% _( k" P1 c$ x: p4 Y% Q
对关系代数的布尔模块
- m( e- f  {  U- E9 m布尔半群, `- |1 g; Z' q5 L- B
布尔环# A4 X# ]  p3 m4 E3 D3 w$ \2 b
布尔半群
, U% u$ L1 E/ T7 n( H8 [! r! ]布尔半格2 C" q1 R. I" o6 F( @
布尔空间
: V) h0 i0 \+ ?+ Y* v" W/ Y有界分配格1 u, Y( ?- Z- L8 E: t+ n/ d
界晶格* l7 ^4 _3 N9 K; k
界剩余格8 k% y; ~- x: `' i- Y
Brouwerian代数
" `3 T. c9 h/ q5 N- W* D4 u6 lBrouwerian半格
3 B- e4 V2 R8 `# _4 H% }/ EC *-代数1 s. L! U( D4 A, W: J; @/ k' G
消可交换半群& Z: o, j7 Y  D4 \3 K
消可交换半群
  \) B1 `* D, F可消半群
) g" P, K9 E& d可消半群
0 _3 `$ z0 z+ s; w- |( \消residuated格9 B; D: [; ^2 }, w2 \/ k
分类
6 `& I& F; q/ L% ]: J' i链
# @) p; G6 T# T克利福德半群
9 D0 L/ v# @5 LClifford代数" V- Y$ X( P$ d! V. x% b
封闭代数8 }* X& y4 \! h* ?, C9 j: m+ P0 [/ X
可交换BCK -代数2 j1 i! F. q& e7 X! W8 n7 H
交换binars，有限的可交换binars，与身份，零，身份和零
3 W; d* [3 [% X/ f& T% y4 k( q可交换的组成下令半群，有限可交换积分下令半群, K; K$ U; h7 A1 ]% I
交换逆半群3 I& v  r7 z3 [1 {" I
交换点阵有序的半群
5 |6 x" |3 [  {交换格序环. Y( j8 f3 |2 z( B- O+ D6 t% B+ M
交换格序半群% Z' q0 i2 J3 s# G% i/ {6 k
交换半群，有限可交换半群，零的有限可交换半群; g  `/ a; M& ~0 l
交换下令半群$ K+ P6 ?% b0 F1 A; m3 I$ o
交换下令戒指1 q) P9 @) ~2 P; s
有限交换交换序半群，序半群
) a* d) c0 y+ E0 r! h3 d可交换部分有序的半群
7 W+ k2 ?, V. u* {: f' N可交换部分序半群6 J/ C1 n( z2 u
交换正则环* [3 G7 W& s" @
交换剩余格序半群
0 K, h- t" G5 p1 d2 m: u9 g9 k交换residuated格
4 S1 I6 _, k: `) G可交换residuated偏序半群
$ b0 a1 B+ k0 N7 O6 Y' _可交换residuated偏序半群
3 P5 z% Q8 R% S9 O- ]. d交换环6 ^, A+ _+ ^0 X* {) E
与身份的交换环0 U" Z0 O6 G, }" S4 y
交换半群，有限可交换半群，零
) j5 X8 G% y# w8 V. z7 q9 y- e紧凑型拓扑空间2 ], k  v2 V9 V3 G4 P
紧凑的零维的Hausdorff空间2 f8 T+ J7 }( l  _& D& B0 J8 j
补充晶格
+ b2 T" z/ Y% |1 I) `; t* ]. _有补分配格' c  X( p4 ]# k; \& X
补充模块化晶格9 A. o% o3 o8 M+ Y3 M2 u
完整的分配格* }2 i+ f& [; n9 S! {
完备格
$ u1 h1 Z9 |( C. o; M+ Y. _完整的半格
6 X4 l# K9 E$ m( L  B8 }完成部分订单. k1 n# B" R. P6 ~6 s7 G  T
完全正则豪斯多夫空间
; \$ I* E9 _- V) a9 s; z完全正则半群, `  l2 g1 {9 j3 `+ r* U
连续格
) M/ l5 X' j9 A3 m连续偏序集
( G0 w5 p, o- k2 z4 g- b6 |% k  V柱形代数) Y2 X8 a( v: _, W  b/ K6 a3 Y& z8 X
德摩根代数; h* U5 Z% u  V  {
德摩半群
- ~& D9 V$ C, k4 v* b戴德金类别
  z  e) V  x9 F戴德金域  ^" }4 `- `! d3 O: f
稠密线性订单+ o# _3 n5 k/ n" B) q6 J7 |9 Y
有向图代数
# @( I6 y7 P2 o  i: d4 f导演完成的部分订单
4 s( m. u7 `7 p; j$ z导演部分订单: _* Q( w  O( x9 e9 k4 C1 E. Y
有向图3 m4 v$ I5 l! B- j( `
Directoids, A9 s8 r  H; c/ |6 v1 r6 k$ C
分配寓言
: Q5 l% I3 o, J0 Q! t, V分配的双p -代数7 a! j/ D0 x$ Y% o# o* [. P
分配的双P -代数
8 J8 `: h* v) ]3 d" }! g分配格扩展
! u7 u- {$ I! _+ d2 L分配格
% |$ Q  ^/ M# [* ^+ ~% H与运营商分配格# ^7 L9 ]( j$ T4 V) }
分配格序半群) U2 q, X7 J; y5 x7 O% g9 i: z
分配p -代数
8 ]4 x+ `! j7 c1 t分配residuated格
# L( p) T% n/ C; ?) b司代数
# \8 S. B( ~' o' n+ Q科环" R( }8 @: T! F2 w
双Stone代数
7 \( Q$ g: \$ }# I8 C+ A* ~' J邓恩半群) ~/ m) o/ f* {; O% I2 C
动态代数
# G$ _4 S$ J9 S) N  V* r( @1 ~6 w熵groupoids
) D8 m8 e0 C% _7 K) T6 K7 u% X/ W等价代数. A  \* [8 `% I# a% Z
等价关系
3 d0 Z4 U+ X) t: C9 b欧几里德域) H& r, D9 ]7 I3 G
F -环. ?5 |% \& H8 I% B* u+ ?
字段
% }1 t% T( ]% |" B# i9 [FL -代数5 N$ T# M+ n" f
FLC -代数6 j$ a' X; `% ?
FLE -代数+ K- q+ W/ [$ f; j, i
飞到-代数/ e/ z0 w+ |0 s
FLW -代数
5 X# l  `2 F! H- ?' H+ @8 r框架
7 O2 }! b4 |- b功能戒指! Q' x4 @$ G4 H3 N0 M* c' `
G - 组
; d$ y$ ^+ }7 D" _广义BL -代数
. L# @7 Q1 h" h5 Q1 |7 `. |广义布尔代数* G3 w# b5 U/ f5 ?' E
广义的MV -代数# W+ ]5 H! i, a; \6 b* T# ?6 n4 v
Goedel代数
' `8 M; i3 n# g+ `( q图
- E) z9 f1 ]6 j3 y. P1 B* zGroupoids
( E% p, X/ c$ z, C4 e8 a组2 e2 ?! @  b$ f  E
豪斯多夫空间
% C0 k! U0 y) g9 N/ _Heyting代数
: i* R2 E/ b2 H8 U5 ^3 X希尔伯特代数
" i7 c0 C; {* R+ [0 A* C3 Q0 QHilbert空间
( ~: K, {, u; |! M- b: Y! |篮球, g2 a+ S5 z5 Y
幂等半环7 E% V. K- C( [# k) O
幂等半环与身份
, D3 u2 w# e- {+ v7 Z/ T幂等半环的身份和零
: \5 v" f4 x9 R4 y1 [幂等半环与零
8 A3 ^+ a* `) O+ t' p% I& l蕴涵代数8 {$ {6 G& Q. x4 u
含蓄的格子
# M0 s4 a/ `7 j0 j' @! _1 o积分域* ^. o& X4 F6 \. G  z$ H3 Y5 T2 S/ z
积分下令半群，有限积分下令半群
0 m2 g0 s, K& ?5 {* W! N/ C- n" d积分关系代数! f+ ~5 p" u- ~- t4 J3 i* x
集成剩余格
! ], O4 {8 t# ?7 M3 s直觉线性逻辑代数% \! M4 K# D$ z& ^; Z# L$ x7 d. c
逆半群  J' E$ _7 I1 @/ d" }8 |- W; Y, U
合的格子# e7 i' t$ w1 x9 f7 b2 u* g
合的residuated格8 Z/ t+ R9 Y. D! p( s" `4 Y
加盟semidistributive格1 ]8 P; \- C3 S& ~% D" j) L& \
加盟半格
0 Y1 {: {9 L3 g  X2 R' j约旦代数  p& I9 q. i) J* n6 Q
克莱尼代数6 `1 e; G  r0 g5 q( H
克莱尼晶格
2 Y; u, V# d5 r0 s8 f- cLambek代数
0 u- t# o, G6 X% {格序群
1 A: \8 L; K7 |格子下令半群
5 b3 n7 ?9 Q' e( j& D格序环4 {6 y9 M; N% o5 }0 m$ }) i6 D
格序半群$ L/ l4 @$ c5 I: Y. _
栅
8 K8 D9 Y, `! w9 s左可消半群
# B, w# b: [9 h& u李代数5 n+ B. R, |8 h% O& `9 T* O& x
线性Heyting代数2 p6 Y+ C; m, t: _& f" i/ `
线性逻辑代数
, L" y( n' j6 f( I( |! ?线性订单2 _  _. `7 P* P2 q
语言环境
0 r: e: r+ r7 O3 n) m局部紧拓扑空间
1 K2 j/ b1 V# F- t4 W& `* B循环; [+ V, L) X) [) u: `6 n
n阶Lukasiewicz代数: l% q- O) T+ s% l) C4 j4 K
M -组
1 _1 Z( S/ ?. @5 d内侧groupoids/ E4 k' F' z0 Z2 S
内侧quasigroups
4 e" G- t* h: u% W$ `4 A4 y' D; O会见semidistributive格
" ?+ m5 r  H. g, @; o+ B会见半格
" H% \  `. `6 @; \度量空间7 `1 S9 z% U! ~* Y' ^1 d/ I
模态代数, G( n7 ]  [2 _/ P- B# @- c- h
模块化晶格& R$ {$ {( I& T# p
模块化ortholattices% |5 `8 Q( k. T% e
环比一个模块
1 I9 Q: T) F9 h8 L6 q9 i9 M. ?- |5 S单子代数
1 j" O% q1 T/ ~0 @0 LMonoidal t -模的逻辑代数
5 j6 ^; l$ e7 [1 M幺半群，有限半群，零
4 @2 x" o; k# E- L1 Q; Z, QMoufang循环* z6 C  C% a- x- T3 Z5 s; V
Moufang quasigroups
3 h& V* ?, `/ h4 X2 H0 @5 Y乘添加剂的线性逻辑代数" z+ R, F5 J( A+ a# A5 q9 H( N4 x
乘晶格
2 m( S9 B0 r$ O7 f7 ?乘法半格* _( `+ t$ c% s" Y
多重集9 M4 M( C+ @3 h2 u/ }+ g
MV -代数
' r1 M! e& `1 N9 Y& @* J* }Neardistributive晶格! E5 p, k) N( q; P+ E
近环
; i4 T4 d4 ~5 Q8 {近环与身份
& V" H  [5 K/ C1 y近田- Y* T; [$ J1 {2 W
幂零群
0 S% z5 `' ~1 @- E! B非结合的关系代数
; N" x$ Y9 ?: |1 H  V1 |非结合代数
2 E, F' e) r# S! F9 [: N$ r普通频段1 I4 I  G# G8 s! z9 X6 a
正常价值格序群
' ^8 A* B6 ]- b+ K4 O0 [4 x2 n赋范向量空间, ?. D: _" ~( x9 k) P7 G$ C. o
奥康代数, n/ v8 g( S3 p+ C9 B0 v+ K- l
订购代数9 y7 j9 I7 E  ]" a% m
有序阿贝尔群
1 a- H: y4 K1 G- Z7 x5 j有序领域( z4 a$ Q& P/ L# w/ B* g
序群
; ~! m0 e- S! @3 n+ S* C有序半群
8 x6 n  a6 ^2 [/ Q与零有序的半群
, F5 m0 e- m8 A% l9 c0 Y# d有序环+ q0 A+ d: u* j0 r8 \
序半群，有限序半群，有限下令零半群2 f- i" O: ^/ W
有序半格，有限下令半格; ]- F% t  H- A+ X$ z) D4 A# x
有序集7 y1 X% l$ j3 U7 `$ c+ a+ b$ H  D
矿石域! C; B7 N# _6 Q( @! ?: `- q
Ortholattices
  Q# a  F- |5 R# k* T正交模格/ h- L1 a) K( q( X7 D8 v* j0 v' j
p -群
; l0 _) p$ F# n& V3 T) P部分groupoids* r. B9 R5 t3 ^4 O, U
部分半群) x. x- g% H1 r, a0 i1 x
部分有序的群体
$ l% ]* A2 s. @/ c) Z! L部分下令半群
/ o0 a3 m9 j7 N% k* y' a/ C部分序半群
# w0 J* ~9 Q& R% Y* k  `部分有序集# e; j# k' p6 o
皮尔斯代数2 v+ ^6 a8 B' S" G# _4 f9 e. }2 P8 Z9 w- y
Pocrims- d$ F8 z  v' A% o" P2 \0 P; p
指出residuated格2 _  C# e8 i7 ^3 H! R& M
Polrims8 m( N  ?8 R/ Y. a2 z
Polyadic代数& N  k4 c) \* [$ q$ [# u' q
偏序集
, d; S) B& z0 Y7 E邮政代数" D7 N; Q* I/ r/ g+ Z$ S+ T1 _% B
Preordered套4 G' X0 ~3 i$ Y, i
普里斯特利空间* ~9 v: k! R/ Z
主理想域
' g3 ]6 X) e& {3 A# l进程代数
9 g# M! U/ S9 r( n2 L伪基本逻辑代数
. L* I: X) B- w0 _  v伪MTL -代数
# R$ X6 G; J% F" I+ |' J伪MV -代数
3 j" r; l! G! B9 P0 {. KPseudocomplemented分配格2 P* \' T2 z8 ^
纯鉴别代数! A7 b6 \4 _2 l1 J9 [, n, @, O5 O
Quantales
; L: N0 Q# C- K: o9 n& j( RQuasigroups: n' X' m3 x7 S3 }+ X5 l; K# \
准蕴涵代数/ p4 z& X* e' ?$ s  h# r1 J
准MV -代数
# B1 L* J, X: H. a, B准有序集
4 r# b( w2 q2 W- E. a' i, }Quasitrivial groupoids' E6 B7 f; Q5 [- k6 D. L; C1 B. G
矩形条带
' p0 |* u: D' f$ G+ d自反关系
9 x0 a. x+ N' B+ |# U正则环3 i. `7 T# `0 I) r3 {
正则半群
$ y: V% ^4 ~0 c8 Q关系代数. x2 v, ]1 c3 }. D% O: i
相对Stone代数" [# U, D& q! n) g# \5 f) W8 d
相对化的关系代数
: Y$ F0 A- N" y; f& L) n6 s% _表示的圆柱代数
0 {/ [) ]9 D% A表示的格序群体* I6 ]0 M; e% t" r) ?! E
表示的关系代数
0 F7 `8 V3 i  ]; @% f3 U% j表示的residuated格
* W7 h' \1 O: V7 \- ?Residuated幂等半环
" ~% B. P5 e% Y2 I4 R% y剩余格序半群- |$ @2 P( l! d" ?" k  ]" `
剩余格3 Q# X4 I5 K" M  h
Residuated部分有序的半群* ~9 o7 g2 E3 H) V) R
Residuated部分序半群
2 t% v1 ^* T# L" I2 _戒指3 R: [$ |% H9 r. d% b6 Y) s
戒指与身份% Y' t. a" r( X: E
施罗德类别
, [9 X8 `5 K- t0 [. U% lSemiassociative关系代数
- [" C' l0 V6 q- W" z. I  zSemidistributive晶格
/ K* c* ?) {  i/ t( o# @* ?半群，有限半群
4 x2 v! ^$ g: I- S9 U半群与身份4 ?& E# \9 ?; v4 t/ v' E
半群与零，有限半群与零, w* z7 T7 J; v! j4 N
半格，有限半格
( d9 p+ \% [/ S与身份，与身份的有限半格半格; M3 l* {8 z% u# k7 n5 @! H* ^
半格与零
( @, w, f) B/ ?; x+ X半环& s: d" S) ^6 C$ f, \) X3 ?
半环与身份. j" l. c, U! t9 L/ y# K
半环与身份和零' ~* ^- c) n5 [: `3 P' y+ k
半环与零
5 |" P* {. l1 k% F% Z4 w连续代数
& n: }# c1 |" ?( z) {集8 S8 ^* z- i9 U: b
壳+ d* n+ k' D* [5 O% {' [
歪斜领域
  g6 n+ F- k+ ~* t  QSkew_lattices2 a% N% a- A$ r' F+ N* }
小类
% C# j- W9 Q) n清醒T0 -空间
3 s- R- i$ z" u0 M6 y' k, ?/ g, j可解群* _6 W. B  ^9 v. C
SQRT准MV -代数+ I7 J  [- y; y# F& O( f) z- `, M; h
稳定紧凑的空间" G, O! a; ?% P# I2 r7 k. N2 \: c) {
施泰纳quasigroups
$ M! d% o) ?8 D* ]Stone代数
* `; f- C7 i$ c" Y3 {  @9 _0 j! p对称关系" n# Q& C3 D* m- ?$ y; N  {
T0 -空间7 m, m  u9 ^1 s
T1 -空间
, G+ {* z& Q$ O/ cT2 -空间! M# r# H% J# q. J
塔斯基代数6 E1 f. ?- c) n6 m" S; Q
紧张代数
, {0 ?" U& c3 i& `: c, K  A; j时空代数
2 g/ W! D5 Y+ ^, S* l& e拓扑群4 t, W; L; Z* n) u) r
拓扑空间
: e, {5 ^# s$ B5 {1 c拓扑向量空间: z8 l" u% b& b5 U  M) w
扭转组% ]. a3 p0 W" [5 L$ l
全序的阿贝尔群  X/ z7 D" y/ |  q; l; P3 P, s
全序的群体* a* U5 }( y$ Z/ E: ]' o0 l
完全下令半群
! p+ b4 \$ _4 P2 a- U+ w6 c: fTransitive的关系
% f& {4 p; ]& b2 g. N9 ?树
( Z4 s  Q  O/ F& u& h锦标赛* u9 g& s' f# q* }& |  {
一元代数4 T0 [, b, w  `! W$ H  P
唯一分解域
/ @0 j7 ~! K* `$ J/ MUnital环" D, U7 j2 y4 s' @3 M" s* Q( U
向量空间
. \. v+ m  N- h; }6 m0 U3 |Wajsberg代数% O; s: {/ g! Z- G1 m
Wajsberg箍" |6 {3 ?( a( q% c
弱关联格
9 S# j7 V/ l3 c2 G% X. D6 K! t3 {) o: K弱关联关系代数
% Z( @' {$ c# Q' P6 H( U& P弱表示关系代数
作者: 孤寂冷逍遥    时间: 2012-1-12 17:03
作者: qazwer168    时间: 2012-2-6 09:42
佩服你，能发这么好的帖子，厉害
作者: ZONDA    时间: 2012-2-14 14:02
谢谢楼主啦



欢迎光临 数学建模社区-数学中国 (http://www.madio.net/) Powered by Discuz! X2.5