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
* Y; |4 e0 F* c! L/ e% a8 ^6 ^
+ Q1 t* W4 z  D0 {
Abelian groups     Abelian group4 N# r* d6 }$ a+ t8 W+ X
Abelian lattice-ordered groups) V  `0 o& Q! p' c4 c7 e% R# K5 r
Abelian ordered groups
8 B* L! S) H: A5 MAbelian p-groups
/ J5 X8 C# X) w5 _1 eAbelian partially ordered groups: }6 u$ _& h9 ?/ |
Action algebras     Action algebra
. H! \/ f% g6 y0 H) W# fAction lattices: E, Y& d' O* v
Algebraic lattices
: X5 u: C9 U/ _* SAlgebraic posets     Algebraic poset* Y' M3 D* B& n, _+ B$ s
Algebraic semilattices( h( \+ G2 F. I
Allegories     Allegory (category theory)) l" @: P# P4 ], N
Almost distributive lattices
* r$ S) x+ u  P/ {$ s6 zAssociative algebras     Associative algebra3 s1 M# |$ A- v7 J
Banach spaces     Banach space' n4 t" `9 \1 _1 Z. s
Bands     Band (mathematics), Finite bands
, x3 M1 f- j6 d: SBasic logic algebras
6 }( O. E3 ]% _BCI-algebras     BCI algebra
3 |! ?( W: v% n' i  D$ LBCK-algebras     BCK algebra
4 {( J' e9 y3 Q4 |3 l/ O4 |7 wBCK-join-semilattices
) I- M9 t2 a6 z0 ABCK-lattices
! u1 F) W# W# RBCK-meet-semilattices* W/ K5 t9 n# H* Q( o
Bilinear algebras
1 O! t0 u- O; D# m$ i* \BL-algebras
8 ?1 v0 E* A' X& F5 r* ]7 @Binars, Finite binars, with identity, with zero, with identity and zero, $ r4 y  G/ f; l3 z  `
Boolean algebras     Boolean algebra (structure)
' S1 h: |" F* x+ n5 i& g9 SBoolean algebras with operators
8 \& p+ X" M9 O: k% O$ yBoolean groups
" L+ |$ K: l& L# `7 C" P) P. JBoolean lattices
) v3 a4 P9 Z( CBoolean modules over a relation algebra. W/ m8 w! [+ H* z& P8 K; S4 n2 V. L
Boolean monoids
1 x/ g2 C" e* o2 v% Y$ Z: WBoolean rings
1 ?5 q. ~9 w1 ^) ?Boolean semigroups, x$ D" @" c" c' w& [7 ~
Boolean semilattices
. q: D* D9 N5 i, e% E5 `' `Boolean spaces( u6 w& _6 S- R* n) y3 Q, q
Bounded distributive lattices
! @2 m- y( E# T+ C7 a; t; W9 aBounded lattices; M9 k6 C( B3 w. V/ |1 K$ l
Bounded residuated lattices! t9 V: e" h9 h, h2 M; F# F
Brouwerian algebras: k2 o/ v' q2 u9 r$ r+ |/ I6 ~+ @+ k
Brouwerian semilattices2 t. S' L: z3 |- R5 p
C*-algebras
( N6 |/ V6 b# b% E; U2 a4 P" a  cCancellative commutative monoids1 A8 R' J- D, E, K  U1 M
Cancellative commutative semigroups, Z2 l' h" u- {4 h
Cancellative monoids
& }& n0 C. ?1 B+ pCancellative semigroups
# b  _! D7 q1 b; y" x" fCancellative residuated lattices) ~* `$ U$ q4 G' v+ {& ]
Categories
: ]) U% H$ @- D* \3 \, Q, H+ T" p1 mChains+ _" a4 B$ P7 ~8 r& C3 [5 J$ v
Clifford semigroups
0 `; t+ ]7 j* x- ~: F) jClifford algebras
: ]8 m' d9 a6 cClosure algebras
: }% P  T* w- V% ]0 w( }4 iCommutative BCK-algebras
8 g5 G$ w0 n) @4 q% GCommutative binars, Finite commutative binars, with identity, with zero, with identity and zero & q& L6 h2 P* p  `7 l% j6 o
commutative integral ordered monoids, finite commutative integral ordered monoids; f0 H. R& V% r& ^1 J
Commutative inverse semigroups
3 C6 ^( ]3 r  U' W. u' ZCommutative lattice-ordered monoids
- r! _" ~' \. \$ ZCommutative lattice-ordered rings8 k+ Z* o1 x4 d9 x
Commutative lattice-ordered semigroups
- z5 X' S, |0 M* L+ M0 lCommutative monoids, Finite commutative monoids, Finite commutative monoids with zero
' {4 G& @+ b" F/ s* `* r! h9 ^' a7 `Commutative ordered monoids
( i" w# K5 M  C- q: w) d9 r. bCommutative ordered rings/ c8 k( h' D8 O4 V- H0 T, v
Commutative ordered semigroups, Finite commutative ordered semigroups* \6 y$ h: V8 e" {. n3 s
Commutative partially ordered monoids7 X1 u0 v) J4 r3 E0 C/ R/ P3 ~, I
Commutative partially ordered semigroups2 i! d2 ?( r+ Q& S) i( q
Commutative regular rings! m# [- |; _8 K1 u
Commutative residuated lattice-ordered semigroups2 y# U0 {" K. x8 |8 W
Commutative residuated lattices
$ ^2 P7 T( e& [" xCommutative residuated partially ordered monoids
: @: Z5 h' ^2 ^# P  CCommutative residuated partially ordered semigroups
& o9 S' N, T. _: d4 P1 h+ ~9 @; ]Commutative rings
7 d( ^4 v- }$ B: @- j' K# L: H" ^3 ICommutative rings with identity/ O# q8 ]( c( |  M; k
Commutative semigroups, Finite commutative semigroups, with zero( e! i  v+ A1 a* K
Compact topological spaces
) J7 b- B' y2 |, r: M# Q- @( HCompact zero-dimensional Hausdorff spaces1 k+ f2 C; i5 D% v' {2 r* h
Complemented lattices
) s5 ?; \: z- OComplemented distributive lattices% T/ \1 U+ g' ?. M
Complemented modular lattices
! W8 U. b% ]+ s$ Y8 `Complete distributive lattices1 f3 Q5 M$ n2 g' M; Y( B
Complete lattices
6 t( r; H9 S% g  u1 t! j$ lComplete semilattices% h' G$ J, N. N+ i( B  u
Complete partial orders" b" c. J' }/ J+ ~  R# F" S
Completely regular Hausdorff spaces
9 h; s) L8 y1 k. \; TCompletely regular semigroups) i# Q. P1 x1 m$ J
Continuous lattices. j+ U2 ]. W# Q: C) x( L8 }+ O
Continuous posets; V0 m' ]  {& A( d; m, A5 W
Cylindric algebras
3 n# X+ ~0 j) P- G' L: vDe Morgan algebras' ^: S/ D3 D/ [" U
De Morgan monoids4 I6 S; l, ]2 x# |5 Q: M! h
Dedekind categories
# E( a7 s1 n; c* b7 ^' RDedekind domains
) t3 ^& q+ j$ ?- F( DDense linear orders  N0 Z3 z% a& M# U
Digraph algebras
3 J: X) H8 E: A, h) bDirected complete partial orders
- W, r, `3 q* k: o$ lDirected partial orders% O+ d: D% Y' V6 D& n
Directed graphs
  q' Q6 n$ ]3 KDirectoids+ h" M1 I$ T3 o" a( p. E" I3 v
Distributive allegories) z/ n8 G3 S8 A4 o
Distributive double p-algebras. t8 j; i& B* P  ~0 g0 |3 U
Distributive dual p-algebras" X) ^( G, I9 g" \7 a/ Q) y3 T6 z
Distributive lattice expansions
6 r& R! V; q/ e( M% m& b$ yDistributive lattices. I# s4 `3 h$ I  m  \4 f
Distributive lattices with operators
; F- M8 \  Z. q8 t: o: {7 p  ?Distributive lattice ordered semigroups
# Y+ X) H  Z/ J; l* r$ cDistributive p-algebras
: m6 @9 s  R' Q7 Q! E! n% n  UDistributive residuated lattices0 J, K: l& S  N- M
Division algebras4 i& C9 a1 @0 L. d; i3 [3 D0 i$ F
Division rings5 Z3 P% ~3 S9 S2 j: v; `, g7 D
Double Stone algebras4 ^; ]& o  G! `( v2 D
Dunn monoids
: b: G% F3 s4 p0 YDynamic algebras
( n+ \  y0 q8 n6 a" @8 vEntropic groupoids8 T3 H% t: j9 R$ o+ s7 n2 g$ I7 o! @: i
Equivalence algebras
& W* X( I" O( p. }; N& XEquivalence relations
$ O2 [) H" Y2 iEuclidean domains; T+ b" F; k/ E6 z) D
f-rings6 G. T0 u/ m' Y8 P2 A7 q
Fields
  p5 y; t/ s" e' a$ bFL-algebras! D7 O! f. d* _3 j7 S
FLc-algebras; `' F$ T* W$ M  y, {
FLe-algebras% K6 n* q. u8 g& o* Q' p
FLew-algebras
7 R$ r( l) o0 `% G+ X: P, R8 UFLw-algebras
0 N2 Q/ \3 G+ O) IFrames' F: N) k- R2 Q/ `; |! S
Function rings; t/ B& a, d, |7 `, s4 u# ?
G-sets
; g% o5 x' i. P6 \& W. nGeneralized BL-algebras
1 W% U4 b2 f' ~- tGeneralized Boolean algebras
" Q. G) Z! y5 i. x& ]Generalized MV-algebras* h; @) X( p( ~! G5 c! q
Goedel algebras7 }; w6 U* L# P6 l
Graphs$ g( U" u; r& G$ ]# P2 b
Groupoids
, c. i, M4 f6 D( E5 sGroups
8 o7 Q: B% |, u  }' `Hausdorff spaces% V; w8 S6 o. z+ B  j' y4 S
Heyting algebras% ?- c1 g7 g, }; ^! m; Z  A$ J9 M* ]
Hilbert algebras
# s0 [) y, V# M& @7 {" NHilbert spaces
+ u* ?: p* q0 {9 z. bHoops" Q" b3 e, Q3 |: _
Idempotent semirings1 r1 Z/ N/ ~& n+ r/ e4 O/ U6 M/ D7 e$ [
Idempotent semirings with identity* [; D& b" |# M0 Z) ~( I
Idempotent semirings with identity and zero/ N# G/ q6 {' ?9 ?
Idempotent semirings with zero4 P4 i" @1 d0 L$ \/ x, }0 O7 p
Implication algebras
4 s8 `( d$ W4 N3 U: U6 v0 WImplicative lattices
( H4 P( g, `$ ]9 P' r) uIntegral domains4 f/ T: t' U! m4 ]3 k
Integral ordered monoids, finite integral ordered monoids
( H4 P8 z1 Q/ @& OIntegral relation algebras+ T+ a6 z; Q" J) j
Integral residuated lattices
# E2 b) c4 B' b& e& @. X0 e" _Intuitionistic linear logic algebras6 x8 X. F7 e( N! ~" c
Inverse semigroups  A. i' @& d# c  G# Z
Involutive lattices
; ~) q( F3 r& g7 R2 E' Q! CInvolutive residuated lattices" o# r. W+ W/ @, B
Join-semidistributive lattices
# J) ]* R: w; l3 M: qJoin-semilattices
2 U4 o) e( J  T' CJordan algebras
3 ^5 `, n* v' t) u/ h7 E8 K0 q6 uKleene algebras
# J# ?0 g$ M; W' p1 V- o" {. gKleene lattices
0 W' h- z* d. }! hLambek algebras  ^4 e& [; Z. p" y7 p
Lattice-ordered groups! k1 C5 G  f/ L( e
Lattice-ordered monoids
/ b* `" M7 X' [- w' _& w; N, N, x! b' o, `Lattice-ordered rings
, O+ D; z& g& n4 u* J; @: w5 }Lattice-ordered semigroups9 V0 }- S* `& p+ [: X, j# ?
Lattices3 M( N, N5 ^2 C6 K, N  o: x/ N* O
Left cancellative semigroups
. k( L& `3 u; C5 N, FLie algebras+ u1 N; N7 v! B- N8 Y7 n
Linear Heyting algebras1 O+ G$ g7 U* Y. t
Linear logic algebras
* d! x4 _8 E, f. ^$ M9 |3 oLinear orders
* I2 l( n# u  [$ cLocales/ v) C2 c3 |0 v3 A- N7 j* y# |
Locally compact topological spaces5 M( `8 ?7 F; G9 R: m
Loops  Y3 D% `, Q4 O
Lukasiewicz algebras of order n
3 u$ I+ w: ?0 E$ r3 vM-sets
' ]& y: Z$ |9 k* K- o  s1 iMedial groupoids
* H% P6 S+ Q4 A& `: Y5 L& o  `: mMedial quasigroups( h) A9 O6 O. _0 B7 W9 R1 E2 O- u6 j: D
Meet-semidistributive lattices1 s+ d1 ^8 W2 H
Meet-semilattices
& x" C# a; P+ F" bMetric spaces
2 |3 z5 u$ }8 P1 Y$ W& {0 Q: U7 s" {Modal algebras
. u. L3 b4 l: D% [8 l; NModular lattices
# i+ ~1 L  ]; B. IModular ortholattices
8 B8 f( _5 U* c; B$ G/ R/ y6 h( aModules over a ring
$ b( ?3 U- [& c, j4 J" pMonadic algebras
8 e) k0 H' \: Q% iMonoidal t-norm logic algebras
# T9 _6 s" k; I; HMonoids, Finite monoids, with zero
9 |' `# h' J8 u! D1 b( sMoufang loops. `& L% ~' s6 {. B
Moufang quasigroups
* L7 u6 k; I% _7 G  c( O, Q% a& sMultiplicative additive linear logic algebras+ b* h' i6 d' A& K
Multiplicative lattices
4 M$ d. ~0 u( k6 k4 l& x. RMultiplicative semilattices& K( k. n# R( h9 g
Multisets
( ^1 n% b  v1 E9 F* P3 I( N, V% |* gMV-algebras7 z: f$ _! m4 K6 X
Neardistributive lattices3 S$ b0 q) H* O+ m
Near-rings* l7 k& f* ~7 j: q
Near-rings with identity
  m/ O9 m8 ]% V6 s& hNear-fields6 M/ `' N8 j# j5 ~, m/ v+ y
Nilpotent groups
! I4 t4 i: b# p, j2 g: N1 k0 G: MNonassociative relation algebras2 [4 x" C3 a' I( L$ m: |9 X  u
Nonassociative algebras
  Z6 ]: G3 i2 I/ W$ Z4 ^2 VNormal bands2 {+ Q2 v7 r) t8 r# H+ e
Normal valued lattice-ordered groups. [$ s; ?" d/ I5 z
Normed vector spaces
7 x6 A9 F* c! i' R/ S0 f0 yOckham algebras
% N' O. q' i  Y- q3 g+ I8 ?) g2 n7 e' vOrder algebras7 X% y6 l) v# [  o2 W  b3 B
Ordered abelian groups) ?5 U! ^! }# S( t' `
Ordered fields9 t; Q2 S' {  O( M3 z
Ordered groups
# o' c: y7 ~% Y& mOrdered monoids: _" B" \0 ]$ x% @: P8 L8 h
Ordered monoids with zero) k  E2 Q" u, {* k2 h
Ordered rings: X3 K/ r  m- y$ t
Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero
+ {3 t+ D* r: @1 `8 Y, lOrdered semilattices, Finite ordered semilattices
! C$ L6 h6 J' K0 W0 g/ F9 E& [Ordered sets
3 X7 ?- V0 `3 g& XOre domains2 `  b8 ~% q6 [
Ortholattices
& [* i5 \2 U& R$ J$ iOrthomodular lattices
& L) L, G0 S' @! _6 o% r" ?3 Zp-groups. T: g7 i! B/ ^# n! [
Partial groupoids4 o2 R: |3 Z4 D$ h5 {2 v5 ?7 Q+ Y
Partial semigroups. Y" ]0 m, w0 M0 e9 A8 Y6 Z
Partially ordered groups
1 N( z& ^; g+ {$ A& K/ WPartially ordered monoids3 V4 I7 j1 S3 O8 [! z
Partially ordered semigroups* s: f7 w3 m0 \1 y- ^! ~/ W7 u2 Z
Partially ordered sets
4 n) G: E3 G" E* y! f+ u( {Peirce algebras
# k) n; U# l: k+ ]) `# cPocrims/ z+ ?; W$ ?$ {+ d* Q1 M
Pointed residuated lattices
; _9 D: y& l3 H7 DPolrims
1 R: \8 @1 T3 W  D* y( D) T* gPolyadic algebras
( u6 t1 c' f7 G) kPosets& o7 @  r& i- F% u
Post algebras/ W) I# x; a& [/ ], Y" W( ^  ^
Preordered sets
! G  |5 `! A4 z" pPriestley spaces( n" o. V3 h/ W0 F; }* P7 s
Principal Ideal Domains% P. e) R" K7 R& N
Process algebras
; P4 n# ?6 t1 m8 HPseudo basic logic algebras
: p. ?' J; z4 L& y% h& a; W6 Q5 a4 mPseudo MTL-algebras0 X" I- l+ c& R0 c& L
Pseudo MV-algebras
9 _$ D, z  D3 LPseudocomplemented distributive lattices
7 u5 ?! N3 X8 q" gPure discriminator algebras: I4 D9 _& p8 k$ ~2 I  K
Quantales6 V- ~0 B  A. n
Quasigroups
. z5 x2 R4 _2 F/ o, v6 bQuasi-implication algebras
' M; V) b0 v# B2 o* ZQuasi-MV-algebra
1 h9 A' n% Z/ P; o  Q9 Y6 `9 w, L: \7 DQuasi-ordered sets' T! h2 u, d# `' L. `! q9 Q
Quasitrivial groupoids
5 B  q% O8 u/ _# S6 k8 I# j1 l* oRectangular bands
- g. N: \7 `  e' `' z7 N  b: }2 GReflexive relations& m9 x% v, E1 ~  b: X' e- T
Regular rings
5 s: X2 w0 }8 G8 |: ^- c4 {Regular semigroups
  l. Z9 g* @4 D5 ~' \. L5 kRelation algebras8 A2 N# n/ }! b! l/ q( l& O% Y
Relative Stone algebras
# _7 v0 n4 z, w# N7 fRelativized relation algebras
1 ]3 d  t7 d! p4 ?) a. rRepresentable cylindric algebras
' D/ A( H6 u; Q/ H! r+ ]5 YRepresentable lattice-ordered groups3 u0 r+ n- |0 S" t
Representable relation algebras; Q$ [* a) w' b
Representable residuated lattices
8 V9 l" j/ j5 a' N' \0 B+ PResiduated idempotent semirings5 C9 |: q& M+ M
Residuated lattice-ordered semigroups! d$ @) p$ @) ]5 b6 C5 ]% V8 ^
Residuated lattices* O3 u) m; T$ @1 `4 N
Residuated partially ordered monoids
+ y7 a  y( n+ i* \5 lResiduated partially ordered semigroups
7 I7 B9 W6 M9 {  @1 k$ \Rings
7 k$ ^* W. B7 j8 G/ \' BRings with identity
+ ~6 M+ x/ C" t/ f3 k" c  PSchroeder categories: x7 S- @" y; s( m& ~
Semiassociative relation algebras
0 b& I8 }: J4 \8 }7 }/ }Semidistributive lattices
- k0 a3 R( E: l+ t) a7 OSemigroups, Finite semigroups
# A5 B( B+ c: N; I6 WSemigroups with identity0 a, v) o& V- R6 _' Q; P
Semigroups with zero, Finite semigroups with zero7 {8 _% `2 x" U0 n
Semilattices, Finite semilattices6 f/ X) b: |8 R+ E  W) o
Semilattices with identity, Finite semilattices with identity
$ j# m0 ?# e# t3 z/ cSemilattices with zero
8 o4 C+ F8 Q' V* gSemirings4 Z# S4 c) b, q
Semirings with identity  y- X/ ~" c7 \6 n8 T# O
Semirings with identity and zero& V% n/ K. B$ a  ], F9 r. }
Semirings with zero
. c8 K5 s  y( p4 g% kSequential algebras9 t/ z9 d4 a4 H: p
Sets
% g# @: H) _7 L% CShells
9 P9 W( Y# D) c. h! t+ }Skew-fields
$ u5 K9 c- u( z9 q( j3 y" `Skew_lattices* V" S! A& ^2 T: g8 _# U
Small categories
) A. S+ J) o- @$ X( s4 xSober T0-spaces
: K2 G" h. o- g3 b6 s' t+ T) }4 Y- zSolvable groups! F; S, @6 z- q4 {
Sqrt-quasi-MV-algebras
  S4 \9 G  z& J7 E* [2 `Stably compact spaces. N% J8 y; m& I& l5 @% \
Steiner quasigroups
4 G8 g: E3 p. @# K$ B+ fStone algebras1 F* n3 h9 E# L
Symmetric relations5 v0 _( n* k. a, Y- ?3 H; M: \
T0-spaces
+ u) o8 \/ @% t  \4 a3 vT1-spaces
# A. Z2 r2 L5 T7 uT2-spaces( B# S: y  B) {6 k+ p
Tarski algebras9 `& o) I2 h  T, W
Tense algebras
1 w0 _5 J- H. H5 Q- [. MTemporal algebras
$ E* J- y- w9 s8 y9 g& MTopological groups
" i: }( ^0 L, G/ TTopological spaces0 G: G2 {+ K6 |+ O9 y- O, p
Topological vector spaces% `: H9 k4 N% ^, S$ f
Torsion groups- o8 k/ r' [0 |' E% N
Totally ordered abelian groups
. q6 @% ?- o$ R0 y4 ]! LTotally ordered groups8 N! d4 w0 j1 _4 S* i$ ?
Totally ordered monoids
: X" C4 `/ t- l/ WTransitive relations
7 L5 S5 e2 f1 |- fTrees  o9 |( J: [7 e6 x6 y
Tournaments! G3 w, S7 S1 b
Unary algebras
( F+ e. u/ M- N" nUnique factorization domains
7 i* Z* L  k& A) ~. ]! M4 _9 zUnital rings( c0 G2 T# p" ^& |* g2 w+ @0 M
Vector spaces
) m7 T3 D, v& ~+ {! W* LWajsberg algebras
+ p2 B6 V9 c  ]% x9 WWajsberg hoops
4 Y6 O3 `, |6 xWeakly associative lattices
# s- U2 E6 {$ w& M* WWeakly associative relation algebras
, }$ w8 _3 t1 Z3 q5 K$ g6 V/ o. gWeakly representable relation algebras( C3 }% S; n; u. j2 u& P% G
作者: lilianjie    时间: 2012-1-12 13:20
阿贝尔群Abel群! y) b1 I; s) g4 c7 f
阿贝尔格序群( M" m8 r( K) Y, `6 z
阿贝尔下令组: C' g/ s. h3 H- V, o9 I3 A
阿贝尔p -群/ v3 q, {2 }* U: _4 ]2 \! w+ b0 L9 s
阿贝尔部分下令组) r2 M+ D7 v" \5 p) @
行动代数行动代数- ^. A5 L# W7 V( g  C
行动晶格( M& s. u2 w3 Q$ F, a
代数晶格! \4 b# g+ y: z  i0 T3 h
代数偏序代数偏序集
, h- o+ n1 O& y' l( M代数半格
2 f- C2 v+ A0 A( V7 j寓言的寓言（范畴论）; j0 \# `3 A  E! z
几乎分配格0 T& ]8 j* F, ^" M* O8 ~9 q
关联代数关联代数: U1 S! P1 Q9 h2 j
Banach空间的Banach空间# Y6 o( L% L% X' s0 P" F
乐队乐队（数学），有限频带; o% Z* S% P( B
基本逻辑代数! Q, }$ I* _) Y  K% v. X' }
BCI -代数的BCI代数
4 ^& z# s5 R! h2 {, I* C) cBCK -代数BCK代数
, `9 n; q) _) o0 u+ [8 HBCK联接，半格
, J; V9 y6 m7 o6 Q. UBCK晶格
) u: s$ f+ ~& D( QBCK -满足的半格+ _$ S; {, o  y4 I) y. m
双线性代数
! x* J- X" h+ d) d" P9 k6 ^BL -代数9 f% h" P: y+ @" ^! A
Binars，有限的binars，与身份，身份和零与零，
' i* a. |: |0 b+ R布尔代数布尔代数（结构）
: }# T' m6 R4 _" j) U与运营商布尔代数
6 f+ a, J% ?* I* [布尔组; O0 p) Y, g8 ~
布尔晶格: x  M! r5 ^4 \1 i0 v
对关系代数的布尔模块* q* h" w# x6 y3 N# f
布尔半群% M9 i- S8 {3 }* c
布尔环
! [8 D1 F: A- y) j, V2 ^# ?布尔半群
+ S0 e% O8 O- ?- l- T: F布尔半格5 v8 j9 m) @* s% o( w+ w
布尔空间
2 l* Y7 N8 t. H- D$ u有界分配格
- r2 V) ]: Y. q2 S, K; e7 R界晶格
1 g" A/ u8 B$ y: d& ^界剩余格; Z+ d+ [8 W9 D8 H, C) h. |9 ?! X
Brouwerian代数
9 R0 V% x6 l  Y) R+ RBrouwerian半格* Z! a& \2 T& g
C *-代数3 k! F8 J% H3 }& I' s
消可交换半群
7 L  x5 M( S( j' k/ }8 s消可交换半群- D7 y$ j$ ^; F. {  }
可消半群% A6 |3 L& w5 |& g5 y2 `
可消半群2 q3 g# G' D3 s" y' s5 J
消residuated格
9 _' p  z+ `5 w+ g# k分类
  w2 l& ~! z3 W链. Y/ g+ O9 ^/ \  m( z3 `
克利福德半群. D2 H% R- v2 L4 s( G' y9 p  t
Clifford代数4 B  P! T" w# n, u
封闭代数
. F, A8 m  ^! F7 ~: q8 H可交换BCK -代数" S7 `  w) Z2 {" u
交换binars，有限的可交换binars，与身份，零，身份和零& F' q% ^  C% R3 k; j- g/ V
可交换的组成下令半群，有限可交换积分下令半群
% W4 M: _+ N. _' y3 l! d* a/ ^交换逆半群
! q5 @/ d$ r" _. I: Q交换点阵有序的半群
3 G) q) A. j1 C) D0 ^3 V交换格序环9 o9 k- ?. e0 j1 y
交换格序半群5 k% ], O3 ~* P( H0 h
交换半群，有限可交换半群，零的有限可交换半群3 o6 C; M& e+ u: H
交换下令半群
+ A  P$ b- h! s$ G交换下令戒指: \/ p, B( x- R5 b7 u3 r
有限交换交换序半群，序半群
3 C3 O( @% ^- ]- b: p可交换部分有序的半群
% ]& D$ K: @2 }1 u( ?可交换部分序半群
" V/ ?5 P6 A+ m. a交换正则环
6 Q' N' M' H" U9 b% |4 y" e交换剩余格序半群8 Y/ c. q! S5 j  J% c: O
交换residuated格& k4 i! {9 X) H4 F2 ^
可交换residuated偏序半群
+ c5 Z- |6 b5 r6 f* _1 v5 m可交换residuated偏序半群
0 B" @1 T5 p9 ~# y7 l6 s& {交换环
1 R( [+ O! ?* ?( q3 L与身份的交换环
* Z/ n0 {  U" e, L# h交换半群，有限可交换半群，零
9 m6 f% j0 c+ p8 P8 E1 b紧凑型拓扑空间
. r1 R/ \+ a& E: t. W紧凑的零维的Hausdorff空间+ G+ w2 l; r6 ?/ ~
补充晶格4 i+ `- A: a8 |7 C
有补分配格
/ Y1 P' w. {! S; U+ N4 S7 q补充模块化晶格
( p. ~8 Q! |( K完整的分配格
! R' T2 x% K5 |8 [* Z完备格
: Z& R& W' J+ f2 }$ {- t) S完整的半格
& ^2 u1 x! V5 d! l8 v' u完成部分订单4 U+ n* k+ w6 N7 S
完全正则豪斯多夫空间$ C2 T+ \: |7 \
完全正则半群
0 D+ f% m/ d0 d, c连续格1 t: r* \+ ]) ^( p0 ~
连续偏序集
* \. T  p# n5 k) X柱形代数5 m: h' t& t. t
德摩根代数
) K3 Y/ Q2 _% E- W8 l德摩半群
* D+ S1 a# u' b! b; w戴德金类别& e$ I  Q  Q5 N
戴德金域
0 N  C, \' L& F! y3 w" S' m& A- w稠密线性订单
# O% B4 s! i! r! }" {- }0 F有向图代数* T! H) _3 Y) _( ^! S9 @1 P
导演完成的部分订单$ _& k$ Y2 ]: X3 f% T3 I
导演部分订单
, k7 Y) i# {, l3 X& K有向图. ?  E& r% ?9 o9 k3 s0 I
Directoids
6 t! c+ y( Y$ E) b" ^; U7 ^分配寓言# E2 Z' x3 B- Y) x
分配的双p -代数
. s" a9 c3 ^6 u$ T% k分配的双P -代数6 d1 m) `1 M5 K' l& Q) a
分配格扩展4 z( m# }" C) ^& R
分配格# U7 H% s  s7 I4 t. u" j6 A4 l
与运营商分配格
1 |9 U0 p; T5 _1 g; n4 y7 g' g分配格序半群  I, }2 g7 j. ^8 x1 }
分配p -代数
; f7 W* _) W8 ^! z& E! j分配residuated格0 @+ j4 H( p( ~1 F& L# `( ^
司代数
8 y) {3 d9 W! X* h0 `# i科环6 M4 ^. p# A# {, _/ O: M
双Stone代数1 `4 o: ~1 W9 n5 b# y! F/ k' L' \6 U
邓恩半群3 B% l6 j: q2 d$ _3 M; K0 J* n
动态代数% ~5 h$ m* P" w+ F! h  T
熵groupoids! q1 v) k) C7 L
等价代数( ^: o# _: o. u- ~; d5 K
等价关系
; a; r2 Z8 y7 V; i8 ]欧几里德域' q- n- J8 t, H2 a8 X8 W
F -环) ?* Y6 r; S- |2 l
字段! A: H5 W: Y% v0 C
FL -代数4 V2 @4 w3 w( r) d) |) j3 K
FLC -代数
  ~' N4 ]- W! P3 h7 G( J! w. |FLE -代数
" X' U# v' y9 R; u0 k, w0 d飞到-代数
, m2 Q" [+ X6 f  o6 x- U5 `FLW -代数  a) m. E& P7 F# r! Z6 @' N
框架8 y- ]# N' }" v, h6 Z
功能戒指
, c7 F, G" N7 tG - 组
) i+ F' Z/ V9 b0 |) j广义BL -代数
0 F& F4 s! P8 O: ]广义布尔代数0 q2 Y8 @1 M. n9 j% Q7 G
广义的MV -代数
/ m. a" x& i% @+ T6 m' n2 }Goedel代数
1 u/ X( ^4 ~( U+ _! E图# |. T! k; ?2 l' M2 S1 z8 b
Groupoids) f) P7 @: }. }5 J4 L
组+ \4 L0 q0 k  R  d
豪斯多夫空间  j8 P: @( N. f4 K
Heyting代数! ?7 a& M7 N2 w7 T
希尔伯特代数
. a  o" P  q! C6 Y' R% _Hilbert空间
2 Q& a( P% u6 n2 J, S6 S篮球% T- M. V$ h8 H' d; x9 j
幂等半环
$ h, d2 O2 G  s, Z# q( I幂等半环与身份
5 q5 P, B4 i2 q, Q0 U幂等半环的身份和零
$ ?( q* f2 q# z+ Z3 d& ]幂等半环与零5 [- c1 J& E' v' R& R- t" z* e% N
蕴涵代数
1 m0 S3 S% ]' ~7 n3 Q" h" E) H含蓄的格子4 u: k/ Y/ h0 |  H7 A
积分域
4 o  d; j2 N5 z积分下令半群，有限积分下令半群
( o: c/ f4 p  E( E积分关系代数
( u' h( }) x8 X3 j" @) s6 u集成剩余格2 X  H/ r/ E8 j. g* ?& J
直觉线性逻辑代数; y3 r" X9 d+ C' `
逆半群
# Y& p" k! C- W6 T! V' A6 O合的格子
3 M% ?, }$ j7 `4 Y. K合的residuated格5 q2 w7 @5 x# L3 `
加盟semidistributive格  v( [: S6 S/ n) d- F1 a/ g$ N( g
加盟半格
, d1 e$ v# e2 w# Q约旦代数. P3 O; l' N/ S! ]% {* i" \' @
克莱尼代数9 n# W/ G5 S6 b) U
克莱尼晶格
; e( e; o+ E( F6 W9 TLambek代数' Z# x6 |; V3 [7 F2 U
格序群
; X$ }" P; D# c格子下令半群8 L6 ]6 N/ c4 k- C
格序环
3 T- d4 _+ d/ R( s& ^. g) {格序半群
. g' v/ {3 R5 N( [% I8 L  A7 K栅9 X: p- \4 N# t! h$ X: U
左可消半群
8 C) i' D9 q3 u" |5 @李代数
6 ?8 f! E+ Z# w# w线性Heyting代数
5 |  m* e/ j3 N# X线性逻辑代数7 |. Y- N. N) R2 R5 J3 F& \, ]& c4 J
线性订单
; O' L, X0 [& C  a语言环境
$ L8 }% g* @3 Z: _# m4 h局部紧拓扑空间
( ~1 P" k! W; N4 s: y+ g循环
) [3 f, \2 C* O4 g( ?' p: b& r' @n阶Lukasiewicz代数
+ t7 S8 W3 b% tM -组
( T& V% P. ~7 Y9 W# d% i1 |内侧groupoids7 T+ Z. k- n% Z. G
内侧quasigroups& e4 y/ u. o9 q& N$ h) f# o( j
会见semidistributive格! D1 H8 t! V; a( I; e, E8 p; v
会见半格4 Q3 k9 p' K: O* T$ W: a
度量空间
; [) I0 K+ a+ ]$ N. k模态代数
+ y' u1 a+ b. l# D; r9 V模块化晶格
+ p! i% I, M5 q5 `# ?  y模块化ortholattices
% I5 `7 P8 a# l% {8 L5 a环比一个模块
5 A  u3 s9 `5 r6 L! T1 y单子代数
) N  _( V5 I8 X! \Monoidal t -模的逻辑代数
4 G5 P8 X0 ]; C幺半群，有限半群，零
. J6 v- w4 q" L8 o8 gMoufang循环
) b2 R" V! C3 {0 |Moufang quasigroups
* y1 Y4 K- v7 E& Y5 M* _5 ?: k) f# |乘添加剂的线性逻辑代数1 P. E- H1 e7 U( V  g8 r
乘晶格: S5 W& v' p$ K
乘法半格* H! v! i8 r; n
多重集2 W1 |( K- A/ P
MV -代数
, d% Z* X" U5 W2 V6 m* |+ x4 yNeardistributive晶格' T1 [6 }! y( D; M- Y; k% W
近环* G& ]- \$ i+ F+ A) B# j- I& @
近环与身份
5 |% j$ a9 N5 O! X$ D! y近田
, {! o& h. j2 ~3 L" o0 q幂零群
  H1 t+ q2 `/ i: Z* |# l非结合的关系代数: A: U- J* \8 ]9 e3 s
非结合代数8 P& I& H1 i8 k0 {3 d$ F8 n  Q
普通频段* G: X7 f/ ]" I# ^, Q
正常价值格序群
  T7 ~1 b9 H5 v- ^  q赋范向量空间
3 G" s3 X6 j- S! e; G+ r奥康代数6 h4 ~: A2 I( [
订购代数" k4 L5 c$ h1 @( C6 z# u1 d
有序阿贝尔群
0 m3 O# r: P2 {$ Z2 `5 W/ y有序领域
! E0 M: z* n! A8 k; H9 {4 {序群! ?+ ]  I& F/ L* E/ x2 [: v2 @
有序半群9 d4 D: |  p$ n$ ^- b! s& }  ~4 |; j
与零有序的半群
4 z- s* Y/ C$ @+ [. i有序环
) m' {3 o- p, j# g0 y3 H序半群，有限序半群，有限下令零半群
& Y$ {( x& {% h3 b+ W8 T8 V有序半格，有限下令半格3 n. k# o' I. P& `& G" K. G
有序集
6 q2 x& l* l& d/ I) |; J1 u8 h0 i矿石域
" C( x9 {& b5 \( D" T- eOrtholattices! [/ H- _" F! ]5 z/ z5 D4 V7 R! u
正交模格
1 Q$ P0 ^; t" Wp -群
6 f$ t/ f% H4 P3 f部分groupoids
. q8 ?% T$ v4 `% [8 c2 x部分半群& A/ m* G7 A% X/ T# e+ i$ v
部分有序的群体
- e) F% Y0 P4 ~; O8 r3 {2 G* `部分下令半群& z5 X- s$ e8 d+ Y6 L9 d3 Y( O
部分序半群2 J5 W) r) g% R
部分有序集
- ^- P+ T2 O3 Y% ?+ m皮尔斯代数9 S5 W: F, y6 k1 o& t; u5 I$ f) I
Pocrims# D% t) v0 r) N5 a
指出residuated格
" f$ R2 c# C( b$ v3 K- OPolrims0 c0 g; X& [0 A0 n6 u7 R
Polyadic代数3 }. n4 x9 w9 v& H5 O# N
偏序集
2 B: ^6 [0 _" z0 Y! ?) |6 R9 E, }邮政代数7 u0 O/ ~$ D2 l. I% [
Preordered套
9 R* Z& V6 i7 s4 K$ z8 a+ u普里斯特利空间
& j( M& y4 q7 k* S主理想域* V" E3 b$ N" N; G" m/ ]
进程代数
5 a- d- W4 l$ L伪基本逻辑代数
" |" x. z( F* I6 ?5 N5 l8 j伪MTL -代数
( \6 d/ O8 W5 L. w' ?! M伪MV -代数* W" ~& o' O# ?
Pseudocomplemented分配格
5 x9 F  q! W% v0 o, T; G纯鉴别代数
, O+ g4 ?3 f, h5 K% JQuantales
1 k3 l9 [( V$ V7 ~% c9 S' Y& DQuasigroups' B! I) ~( J8 U# ^) V
准蕴涵代数' a! z# v( Q3 A" w
准MV -代数5 U; a2 ~6 |% T$ _6 [
准有序集
9 Q& P4 l: H2 F4 ?; }Quasitrivial groupoids/ ]+ F" T0 D1 d6 {
矩形条带+ O& W, c/ E9 W" L* J) I
自反关系2 O& M4 W$ l2 y  c  c4 `
正则环
: z- ~( }# P/ W. g5 f2 x正则半群
4 Y* a# }! J9 t, a% T关系代数
) o4 E9 i* R6 w! l4 ~相对Stone代数
/ l! \5 H( O- `  S$ m9 l相对化的关系代数
+ W4 Q# q0 _6 \+ j9 n7 J表示的圆柱代数
3 I8 F6 p  Q& [; v- s表示的格序群体. a9 s- j$ D9 n4 [
表示的关系代数; T9 D4 o! u$ B8 ^6 `2 N
表示的residuated格
2 H& [7 i, W' S# s  f4 B, ]* |7 p9 QResiduated幂等半环
! |, c( y5 C& X' A2 ^4 a- |& p0 K剩余格序半群
2 S. _- j8 e0 p+ v' ?剩余格; P* N) y* z% |. |
Residuated部分有序的半群8 B7 a; n, X, \6 E. Z6 C
Residuated部分序半群7 X- z6 x5 F1 h, b) |
戒指
- h: B  F! d# d. u5 O3 n# y戒指与身份
( }. d- ~1 r1 h) J施罗德类别
% f# q' j9 k3 |- I$ S% g  G. z0 c" fSemiassociative关系代数0 y/ ]8 W5 {0 _* P2 C+ b
Semidistributive晶格( o! m: P2 ?# A: F
半群，有限半群
4 G3 R  G* L3 ?: T半群与身份
) _3 ~! M- F/ n; d  D2 P半群与零，有限半群与零4 h* j1 Z1 J; K6 g- q! |
半格，有限半格, }1 {8 ^# K2 V
与身份，与身份的有限半格半格5 c, X4 p: ]: h2 R
半格与零
% V$ b5 N: m5 X$ F4 ?( `/ K& ^半环9 Z' V4 `% \4 ^/ c8 |, Z6 x/ A) K  d
半环与身份
- O- T7 A6 Y  g9 e8 h4 j/ w半环与身份和零
3 V4 ]5 {1 r, w" M半环与零
' }; W( q  ^4 t连续代数
; E6 c" _( [. r1 [1 H3 p集3 N' S* R7 _1 B1 {; [# V
壳, C4 f# M, ]1 r; y% G% l
歪斜领域
7 P+ W+ I* l  ~* h1 Q9 O0 YSkew_lattices, _4 g& V' N! K% [. h1 O, G0 D
小类
! \4 W. ]4 j& a* N+ u清醒T0 -空间  T! [* h- q! G- \
可解群7 h. c/ o) m1 J- v7 F* v' Y! M0 D
SQRT准MV -代数
* B2 K* l' ~! I: f4 b  k稳定紧凑的空间
9 F% L, @7 |: U7 z- p施泰纳quasigroups
) D& A1 n: r) k' y. S$ y( J$ m% GStone代数
8 f- r. t: X$ R8 d! g8 N对称关系
) Z* _4 r- a/ e! ]9 B2 o. `4 q1 G/ o) xT0 -空间
' M5 T) V: U5 d* j3 O, c  RT1 -空间
+ J: H3 n, `! z9 YT2 -空间; n4 l* o7 q( \" B, s0 q2 G- b! s
塔斯基代数1 _: y- M) \9 T  }6 d
紧张代数7 Y+ K. _2 ]( t8 d/ k
时空代数1 D7 d# G" l  a& }. y' E3 r
拓扑群$ T' F% u- X2 E; O& ^
拓扑空间) W" q3 `2 I. [) H! n% C2 p3 l' X
拓扑向量空间
) ^9 x0 E$ _  E7 s! ]扭转组* I; Z2 j) e3 h- g' O/ }
全序的阿贝尔群! e2 s) g6 d8 G* Z: y$ B  D2 ^: ?
全序的群体
5 A# u7 f! S1 I5 }2 w完全下令半群
1 q- u5 N' z# U7 G' ZTransitive的关系
; j+ n1 ?' I. E' D' ~* Y树5 @8 Y8 b( s  u/ u9 b) s- e
锦标赛5 ?( t! I% |/ D0 ?$ ]
一元代数
! n4 {5 v5 g7 \' ~: L8 m. l唯一分解域3 v& u% C' A+ i- O( [+ `" b6 W
Unital环
: P# m% e, y/ ?- r* x% s9 |! n) K& V向量空间% b. s, ~' [" S) n& |
Wajsberg代数
9 ~) M: {, n9 @% |3 lWajsberg箍
. L  P1 c4 Z% F0 O. A/ j弱关联格
; x& ^# W/ f* z5 \# G5 [! R( y弱关联关系代数
3 a! M7 b% V8 K& d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