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
/ L& S6 h& f4 d# X# `
' J  E/ V8 |7 [& j9 i2 _
Abelian groups     Abelian group7 \9 t# \! [( E' O; j$ l  B
Abelian lattice-ordered groups
: L& R0 x% s4 P5 c7 I* d$ TAbelian ordered groups& m. K* x  q( s2 V
Abelian p-groups9 x: z2 j" a& t1 n$ S/ h
Abelian partially ordered groups  A8 w4 O) X9 r# d5 J* R
Action algebras     Action algebra
# w! Y3 n9 Z. i" p' eAction lattices
  a! f$ P3 I6 O- a$ J  |2 u) MAlgebraic lattices
$ ~% |: s0 n2 ]4 }3 qAlgebraic posets     Algebraic poset  T9 i* T  d/ p9 E, m& i( _1 U/ Z4 \
Algebraic semilattices
/ D- q4 s8 j1 K. U: N1 W1 YAllegories     Allegory (category theory)
( R; g) ?: g/ x- ?" h5 nAlmost distributive lattices0 j4 G( ^% u3 P. I
Associative algebras     Associative algebra# e0 u! M, x$ [" ^+ x, x
Banach spaces     Banach space
: }6 p5 @  v( k9 z7 r8 v+ c# yBands     Band (mathematics), Finite bands
( n+ L: d$ U7 b$ SBasic logic algebras) a0 c$ N! q/ q- @" N/ ^/ I$ [! _
BCI-algebras     BCI algebra
; x0 T9 s, Y9 E0 M) ZBCK-algebras     BCK algebra( k' N" |/ Q$ _
BCK-join-semilattices$ j& v1 k( T! g& F) t+ W# {$ @
BCK-lattices, `/ g8 \$ p2 u; {7 n
BCK-meet-semilattices
  p# L# u5 P: H' |+ GBilinear algebras% }8 u" i, ?1 Z" G. o
BL-algebras, y0 z& W5 U% F  P' E0 n8 g, e
Binars, Finite binars, with identity, with zero, with identity and zero,
3 ]& t& n0 _* @! |6 ^( o7 Y% }5 Z9 iBoolean algebras     Boolean algebra (structure)
) V" S) J- s* PBoolean algebras with operators
- S' R2 _" o  c& YBoolean groups
% x9 f, ]+ r; G- {7 JBoolean lattices
! B8 L5 x; C; V& x* EBoolean modules over a relation algebra
6 }4 w# a8 O8 I$ }' }0 JBoolean monoids
" n' B/ j/ T2 |- o  ]) Z- ABoolean rings1 e+ l2 \0 J( e7 H1 i7 y
Boolean semigroups
% n' D2 T- t  m7 [" N9 @/ yBoolean semilattices
+ _1 C5 x2 e. @8 e; K% N# [# |! `Boolean spaces' X1 k4 e3 g- ~
Bounded distributive lattices8 h# O3 n- }0 ^+ F
Bounded lattices
9 S- O! a, A) {# sBounded residuated lattices
$ {; i% {' j+ o% ~8 G3 F1 }' KBrouwerian algebras
" P! {1 d$ U+ `+ b' [5 w9 ~Brouwerian semilattices
$ j9 q$ }  O" K) P* DC*-algebras
: |+ k6 d, s* d. wCancellative commutative monoids0 L( I, T% H7 c& m' v  O% N; c
Cancellative commutative semigroups
8 M- L0 U1 O* hCancellative monoids
/ }% d" D) J  o2 P! P6 `$ L0 S! BCancellative semigroups1 [% I! O, ~2 P
Cancellative residuated lattices9 u: Z3 u! D% F' Y8 B
Categories, B* ]) i1 L0 G) E" d, a
Chains! x+ T; ?1 A, U: Z7 b1 v* c
Clifford semigroups  y+ o( p) `6 r$ W, R( j9 p
Clifford algebras, m4 n7 Y* o; g7 [; @, s
Closure algebras
) D" F4 {8 {/ rCommutative BCK-algebras' t% S# u. Z7 U/ u( b* E
Commutative binars, Finite commutative binars, with identity, with zero, with identity and zero
" j" x0 Q7 [: b/ b% |, ]commutative integral ordered monoids, finite commutative integral ordered monoids, q7 ^9 D' s+ k& }" b& J) x
Commutative inverse semigroups) k7 r# e- t& |4 ~! ~
Commutative lattice-ordered monoids& }1 P& [8 o' ]; q2 r
Commutative lattice-ordered rings
* \1 R$ M9 h! G) o6 w. TCommutative lattice-ordered semigroups2 A1 t5 l! \7 Y
Commutative monoids, Finite commutative monoids, Finite commutative monoids with zero
. u9 a; l* F2 [+ q' _: \$ p2 rCommutative ordered monoids& C; @6 Z: P& E. t9 Z
Commutative ordered rings
/ M* O& p2 e7 I0 sCommutative ordered semigroups, Finite commutative ordered semigroups- Z( h% L6 h2 N$ Y0 [
Commutative partially ordered monoids) u, K: \9 U; X
Commutative partially ordered semigroups' t, M6 L2 b6 o# j6 h
Commutative regular rings! c! x% o& W1 r$ p: A4 H& f
Commutative residuated lattice-ordered semigroups
3 a9 T7 E8 [& _% NCommutative residuated lattices) `9 }7 [9 E- s# Q* R
Commutative residuated partially ordered monoids
* k( l6 ~' q# PCommutative residuated partially ordered semigroups4 O( c5 n  U. P7 o# H0 y
Commutative rings# ]: b2 g; F$ j; l" l( e9 I
Commutative rings with identity
4 `; d# ]( Q. ^6 c) Q5 NCommutative semigroups, Finite commutative semigroups, with zero
( }* n/ ^$ |; wCompact topological spaces" h* f2 l- d. B) q% ]/ q. j0 ?
Compact zero-dimensional Hausdorff spaces
2 S* M; ?, E2 d0 AComplemented lattices* u& {! }" K( I3 l" x
Complemented distributive lattices5 {6 S/ z" j2 H' h9 F
Complemented modular lattices( F. T9 _. w( k* E5 R
Complete distributive lattices' }; g( F' x* w9 \
Complete lattices
1 r0 ?% p) U! QComplete semilattices; ]$ s1 ]% c9 `8 q5 I& z, l3 j+ o* f
Complete partial orders; v/ @( Z5 P- ?7 f5 Y3 z
Completely regular Hausdorff spaces
3 s9 [; [8 \: [' L% g, xCompletely regular semigroups
1 Q$ J6 q! f* g) o( H3 sContinuous lattices% Z; d5 O5 `0 g& ?
Continuous posets
( d" z2 N1 g' LCylindric algebras6 y5 I# S. K+ b) r: p" b! c
De Morgan algebras
3 g6 K) L6 g, Q7 b! }De Morgan monoids
% o: w' \, }) E2 g; {' ?* aDedekind categories2 O" E% L! W& w) }- R* M6 q
Dedekind domains
1 c9 a  }: c' s9 U+ Z/ E" z% v" Y& qDense linear orders
2 B# v. N: d; V& e1 a7 x. VDigraph algebras7 G, r' F* m7 w2 G1 y) g# [5 C% W) [9 h
Directed complete partial orders
! W. R& v' Y8 I2 c5 F. vDirected partial orders- @1 W1 R# j, A* z
Directed graphs
! B- Z7 i5 v/ O: X1 HDirectoids
+ K% i; ^7 R" u- ?# }6 FDistributive allegories2 I8 T7 T+ d( ?
Distributive double p-algebras7 I, k/ n, ~& r( N+ j( Y9 b
Distributive dual p-algebras
% O& B, P0 T8 V1 E1 D: U" GDistributive lattice expansions: H5 t5 b& M0 X$ {+ r
Distributive lattices
2 O$ O( p2 A( Y; C- ~9 yDistributive lattices with operators
# H( ]: r: m% k& J, a* N+ t: P1 mDistributive lattice ordered semigroups
5 {& K+ _# t# ]7 t1 Z+ y3 k7 EDistributive p-algebras: k/ i6 j$ n5 Y  D
Distributive residuated lattices
$ d9 l/ `2 A$ lDivision algebras1 }. d1 B2 b4 k: e
Division rings7 d  u' S/ j- ~! t
Double Stone algebras: z( i! S8 c6 A
Dunn monoids, Y2 L3 J$ y0 _
Dynamic algebras9 X# U) [: k8 _1 t8 S0 `4 b
Entropic groupoids, {  b! `/ Y' N) ^) M) x% P
Equivalence algebras6 {/ q$ H3 W' K! R; E+ B
Equivalence relations" t& z$ c; g/ b
Euclidean domains
  g6 W" j$ V! g# G6 Yf-rings! O6 }" X* g; g
Fields0 v: b. z5 Q2 a. i, y
FL-algebras) G6 Y$ x4 S* |* f! g# I9 ]
FLc-algebras: I1 z2 R( I8 o! s( `6 Q3 _: Q# v
FLe-algebras
6 m2 S- _4 q* g. OFLew-algebras
5 g- L. c3 T* V9 C0 Y$ W8 ?FLw-algebras
- n0 z; |; b" YFrames
& @5 Z5 L: ~, H% u* UFunction rings; h- z6 N: f9 X" K
G-sets/ V, Q1 D% S+ k1 f. O. f% }
Generalized BL-algebras8 O* }# `7 T5 p! h9 |) ^
Generalized Boolean algebras; ?1 W4 U$ b$ {% ~; ]  ~/ @; |
Generalized MV-algebras
. Z8 q+ p# k* W2 ]4 j- oGoedel algebras
6 m( m7 O# [" q% WGraphs( T0 Z0 j1 r& K
Groupoids) w3 i3 b+ s" Z: r. P5 ]' E- I
Groups
5 D7 n, |) h4 s+ ]# tHausdorff spaces
4 _6 e# M* Z! Y0 HHeyting algebras1 @: q2 [& G& y, f! q9 Q) _6 n1 k
Hilbert algebras, E9 a$ h2 X5 `$ C
Hilbert spaces6 @: {/ S' w8 g6 }
Hoops
& S! }( \% b+ L; ]7 H% KIdempotent semirings
. ~) g# n: A. s3 d3 e* hIdempotent semirings with identity
) a! h' i# r* j7 S7 gIdempotent semirings with identity and zero9 p+ Q# e6 @# b# Q
Idempotent semirings with zero
$ Z1 x% e+ A- wImplication algebras7 V) n1 u, Y  w: X8 e' G* B1 @4 P
Implicative lattices
  m9 Q+ t/ J3 @/ TIntegral domains3 }) g; G" ~' q! _2 v; c% E
Integral ordered monoids, finite integral ordered monoids
7 ~& s/ C! S' b* U$ k/ a( yIntegral relation algebras# T7 G/ d# |( f; _6 R# m2 \
Integral residuated lattices
! N3 v; e7 l3 O- p9 g. A  n$ U" sIntuitionistic linear logic algebras
& b; E. R9 b$ r% @, A5 NInverse semigroups
# @: R% M. p( t3 N- k' Z4 i7 L+ m; IInvolutive lattices- m2 T9 t# v# F( q5 Y
Involutive residuated lattices
+ v  q& X% E! O* y' A! j$ kJoin-semidistributive lattices
" W# d6 E7 {; O  a+ H6 qJoin-semilattices
. V7 p. I& l, ^; L6 J% @/ NJordan algebras
# ^# c/ n3 [. `9 e: w: h0 oKleene algebras6 S! c/ t- w7 Y4 U# }$ O* e# s
Kleene lattices
5 E' X2 ~$ a9 A" |- q( wLambek algebras
' z& }$ E, t9 m: }Lattice-ordered groups# u9 T( D  [: d9 t. I: j
Lattice-ordered monoids
+ |' V6 ^0 D0 h+ ]Lattice-ordered rings
; W) B3 L4 p2 @7 W5 VLattice-ordered semigroups+ E9 f9 m' w) P8 i* o
Lattices" P5 _" ^* g2 E. I9 k
Left cancellative semigroups2 t8 l: {3 O+ m5 L9 J- q  E
Lie algebras# ]2 r/ v2 Z4 D  d- Z& f" h& w
Linear Heyting algebras
4 ^3 P9 P) e6 C6 l) @6 p* U- xLinear logic algebras
1 k5 v0 j/ F9 mLinear orders
+ v6 B8 }8 G: w' |Locales" a% N# [4 f9 F. Q  g
Locally compact topological spaces2 ~6 Z* Z: D; n1 c6 i
Loops/ A5 s/ x+ Y8 I* X/ z4 [* Q
Lukasiewicz algebras of order n4 d+ a9 X4 B' u& Z6 x
M-sets
8 F2 O8 ?# o$ t2 l. f0 s- i. l' VMedial groupoids) M1 M( }4 A5 g! l4 Z/ }6 f, L! [( T
Medial quasigroups
3 Q4 z4 Z) W. O+ f. p4 vMeet-semidistributive lattices
4 A; [, m: B9 q7 r; HMeet-semilattices
7 l6 K$ ^: M$ [Metric spaces
& J, ~: t$ @% e, v' PModal algebras6 {8 K; B4 w! T( |
Modular lattices# i$ n" m# M3 H
Modular ortholattices
$ Q% j! V2 Y5 d+ i4 WModules over a ring
; Q6 C  D. ^' ]7 K/ i  gMonadic algebras) }0 c  P$ g, F- o" V5 ^. h
Monoidal t-norm logic algebras) o0 S$ z6 G; \
Monoids, Finite monoids, with zero
+ Y% Z4 M( v1 r( t4 C& R+ KMoufang loops$ n% E4 t* {# V. ?* N* h) U* J+ P
Moufang quasigroups
( X: Q0 q! Z+ a8 dMultiplicative additive linear logic algebras
  d: F" H; [: q6 j4 o" TMultiplicative lattices$ e$ `9 A0 N$ C5 L: R: R- N" i
Multiplicative semilattices
* O, R0 ^6 i# Y) u& T  X7 u  oMultisets
( W& ]3 J" n) PMV-algebras: d4 q  G5 `3 O9 _
Neardistributive lattices
( B) G  ?+ v0 x* |) TNear-rings
- r& b' W- f5 u7 C7 h8 \Near-rings with identity# `3 Y3 `- m$ N, O
Near-fields& v/ X- V( g1 ], x4 Q) E
Nilpotent groups
# z$ `2 Z) K) x- NNonassociative relation algebras
" C  N$ Y( w" l8 c7 f( y/ QNonassociative algebras3 o" n8 h; t& C- n
Normal bands
7 u( H" b" b2 y7 R6 JNormal valued lattice-ordered groups/ z& n9 l/ M. U/ _
Normed vector spaces
( `7 H8 Q4 b* e0 v! y; s4 HOckham algebras( D) t5 v) L, H; s) J) @
Order algebras
# {5 c9 m$ ^0 d" h, ]Ordered abelian groups
* U* B: n8 K2 q- }2 t4 h- kOrdered fields$ d( _0 y0 I8 L4 Y2 \9 M- \
Ordered groups
3 C: s' ~8 S6 q% G6 n$ k6 TOrdered monoids- p! n" E$ n4 T1 G1 D
Ordered monoids with zero
) b' s4 Q0 t3 L2 L7 V6 tOrdered rings
$ `$ E6 {3 `  TOrdered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero
! O; }# T3 N4 N( X9 hOrdered semilattices, Finite ordered semilattices
! d4 U7 ^; U/ B& {" R( aOrdered sets
. X- n5 S, N5 ^Ore domains4 z1 d2 N1 E& q* E/ i* i$ N5 a3 Z
Ortholattices
( r4 y8 Y1 w8 k4 F/ rOrthomodular lattices$ X7 N8 f( c+ [: D& D$ W
p-groups: \7 |; R% x) q! C  \- B7 i' A
Partial groupoids2 @6 U) G  x( z5 p+ H# f
Partial semigroups
' h4 v2 N; M; {9 I# D+ Y/ g) NPartially ordered groups
6 K) c! o; C- h& K0 uPartially ordered monoids
4 G7 h; M' S. W+ j- W) G, c$ SPartially ordered semigroups3 p# q5 F0 I" D" B5 Q8 U
Partially ordered sets5 E# n% c' I9 D& a. {
Peirce algebras
2 H' p7 Q5 \9 y. ~5 XPocrims4 p% Q. w% X" ~- L5 ?# L
Pointed residuated lattices! T* r7 M6 ~2 Q" |" J
Polrims
' i, J& `+ H5 FPolyadic algebras
9 h1 L( Z9 X8 L; d- RPosets
. D. Q8 s/ X8 A7 s" `6 XPost algebras
8 R9 ?. R0 H" yPreordered sets1 L, c5 R4 s2 f  n: L
Priestley spaces) x3 J# m) c$ I( T) _. G: u5 J
Principal Ideal Domains1 [6 l+ w; l; a  h
Process algebras" n% I+ J9 t) e2 [0 B
Pseudo basic logic algebras! I; Z+ Q, T( k* t! z
Pseudo MTL-algebras4 U2 L. D3 E& W0 A4 K1 ^
Pseudo MV-algebras
6 E  S" @$ m7 q7 P! q7 TPseudocomplemented distributive lattices. n! p# g* `0 S) Q
Pure discriminator algebras/ W* C& w& m3 M& l- a4 |' \
Quantales* Q" Q: E$ }8 |! U0 h
Quasigroups! z- M& L9 v0 q% t' S: K" c
Quasi-implication algebras$ M" z7 M. D0 j3 C; |  m
Quasi-MV-algebra
# t3 g) S: C$ @" KQuasi-ordered sets, m; x5 m  f9 ~; Y1 e
Quasitrivial groupoids/ c' S' _9 @( J7 g% M( Z  I
Rectangular bands) d3 G9 o, V& F* y. j5 _9 ?
Reflexive relations* y5 U: e2 z  Z) d! w: [
Regular rings
" f5 w6 D, k5 f5 {& C1 RRegular semigroups
0 u' F; V7 S2 _; S* J. X  ~Relation algebras
4 F9 R) T; W+ DRelative Stone algebras9 D% Z: m: g- n& H9 K/ [
Relativized relation algebras" X2 V( B" `4 [7 ?; q0 [6 P
Representable cylindric algebras9 P$ D* g* G! S) q
Representable lattice-ordered groups
4 P* {: Q# p- d' ~! DRepresentable relation algebras0 y' i. ^1 G; b/ A% @: K8 Y
Representable residuated lattices: N, m9 k/ i; W2 F% y$ {
Residuated idempotent semirings
  ?' A" ]6 p3 v1 HResiduated lattice-ordered semigroups8 `5 w% b: B+ C
Residuated lattices3 J7 q9 S( J1 t: x8 {
Residuated partially ordered monoids% B* B9 z7 Z+ J( a. w8 i: e+ e* @
Residuated partially ordered semigroups
4 V( i6 R- Z# p. c& t: d/ ZRings
! v+ Q, Q+ b; T  f0 h- nRings with identity
2 y& C& k- A$ d5 U2 D0 [5 XSchroeder categories
  b  w0 m- Q4 l0 ASemiassociative relation algebras4 N  i5 Q2 d6 a9 j0 n9 q
Semidistributive lattices
6 ?2 A# k) ^6 d- z. d. Z+ J9 USemigroups, Finite semigroups1 b. X  D7 J# D
Semigroups with identity
8 |+ a% w- ~) C; F6 o9 oSemigroups with zero, Finite semigroups with zero
; l+ \% z2 q' G& |4 sSemilattices, Finite semilattices' Y( w" D5 f# f
Semilattices with identity, Finite semilattices with identity1 ~* _3 W* U" t. L3 p, n
Semilattices with zero
7 o+ X; _, h# j! F  oSemirings$ n- T# O# U' _2 F. O- H
Semirings with identity
) L: s; y! z2 G2 P" s! U: aSemirings with identity and zero$ w2 ~- P! g) n9 B
Semirings with zero$ [! r% S9 x$ }- z; Y
Sequential algebras0 M+ J& n" Y- @* ~
Sets
4 _2 F! |0 S3 b/ lShells$ J6 }2 |% |5 _2 j; [
Skew-fields
! g3 l2 O/ u( `. pSkew_lattices0 |' l; ~- @0 S9 [% ~" E
Small categories
0 }2 S* E: @. f! u1 R) F4 sSober T0-spaces
# L; S' u: ]( J- vSolvable groups
# y5 H3 S: ]$ `( U2 v$ h0 cSqrt-quasi-MV-algebras
" ^9 e6 F; g( x1 C) ]$ vStably compact spaces) I% j* x+ V- ~  Q2 w
Steiner quasigroups
- {* P5 N; x/ S$ x( v" \+ H- lStone algebras
. D% x. ~5 d: nSymmetric relations: y4 E* }2 ?( L2 p2 s
T0-spaces+ h6 @/ W1 I1 x5 c
T1-spaces. @3 s1 s/ u. q7 l  B
T2-spaces; {9 Z/ ]' \; }2 m- A0 _! ~$ h, ]
Tarski algebras
  ]% E  h6 g6 o" }9 ETense algebras  j5 }. C& }7 B. d, ~) ]& w
Temporal algebras! o& K2 w5 ?8 Q9 x+ j
Topological groups
  e3 h2 x/ t7 P, uTopological spaces
9 k9 Z+ o: @; v* L1 O1 r8 XTopological vector spaces0 a8 l9 U6 O$ d9 D" `4 s
Torsion groups
% S7 R9 {- }7 C# r3 nTotally ordered abelian groups; q* Z2 L4 P' }+ f; i/ E1 Y
Totally ordered groups
4 M: o: i/ z4 k; M# b" sTotally ordered monoids
, \% s- {) l! ?Transitive relations
% H9 S' f- h) S  g' {  l# STrees
( |. h  @* O5 \/ K0 n8 |Tournaments- ?& a' |: K' i
Unary algebras" j8 Q7 _) E8 e# h, E- ?* ~7 p5 |
Unique factorization domains
+ b  W! j& D: u8 PUnital rings
. r2 T0 b" g* A: BVector spaces
& X- H% u4 C; j& i) k4 eWajsberg algebras9 b1 ~+ E- z4 S: L+ A1 r, M2 f
Wajsberg hoops
* w% r6 t$ K9 l: P$ ~Weakly associative lattices) \1 {  v, B; x$ L6 r+ W* H
Weakly associative relation algebras
8 Z# ?& D& A$ a/ Q3 _9 NWeakly representable relation algebras5 s0 L5 R" v) h) l  ^
作者: lilianjie    时间: 2012-1-12 13:20
阿贝尔群Abel群4 S" a. n, A1 @6 j5 ^; z
阿贝尔格序群( ?5 q/ a; e2 }2 Y8 I
阿贝尔下令组" r1 D3 {3 w2 u0 T
阿贝尔p -群# g3 V# q7 }3 @4 f4 T4 B# t: n8 T
阿贝尔部分下令组9 i% Z; h* F7 U
行动代数行动代数1 q4 @  t4 u! X# }
行动晶格
2 s) t' Z3 `* d2 B: E代数晶格
" H) D3 r4 u! O) V5 c代数偏序代数偏序集
; G0 K  l; @" C! X$ Y代数半格
8 l4 _. E6 X2 K$ x! }* V8 |寓言的寓言（范畴论）
9 A6 ^+ U  I; C几乎分配格% S3 k1 p6 c% r3 M7 i- R
关联代数关联代数
$ q2 L" x, X" LBanach空间的Banach空间" G" _, F' i; f3 Y
乐队乐队（数学），有限频带
+ K7 U5 @# U% f$ Y1 A3 {基本逻辑代数
  `& l# S7 M2 eBCI -代数的BCI代数2 \5 X' i, L" c' f) ]+ d
BCK -代数BCK代数
3 r9 z# d' D% s+ o7 `3 Y6 T% ?+ oBCK联接，半格
3 W: n0 `5 B7 Y: E' rBCK晶格9 D/ m# [% x9 Z, V, n, y" q
BCK -满足的半格: E9 k6 v# @3 V6 f3 J
双线性代数
3 c" W2 B% B0 F- K# EBL -代数) I: f$ I3 O0 X" O0 d. q$ D$ D: v
Binars，有限的binars，与身份，身份和零与零，  I" _9 Z" q+ U1 w& N* b  n
布尔代数布尔代数（结构）4 D- q& G' k; |+ J7 A9 v
与运营商布尔代数
6 V8 D" M* M; p3 A. v" S8 H) P布尔组
/ v6 j) v" _0 ?) |$ \0 S9 C1 h布尔晶格& C& A" j" d8 h/ f$ c7 j
对关系代数的布尔模块+ X& m, J2 X" i
布尔半群1 W9 K; i7 z2 k, M$ o, r3 i
布尔环
  k* ^  w: q& q: ^$ j6 I  U, U布尔半群) S% I$ a2 }; p
布尔半格1 H* \+ \! F4 h9 p0 _
布尔空间" ~! `3 P- g! T' Q( y) R
有界分配格
1 F/ S3 c$ }! b- ~( e界晶格% m. D8 ]: ^% G4 b3 T  u
界剩余格! c. z# X: ^! g* y/ x. ?
Brouwerian代数& |; }# u/ s. }3 S9 \  S9 f: z; Q
Brouwerian半格
. C% ^0 P8 }. d2 kC *-代数9 V6 V5 s5 h( V
消可交换半群
( Y6 \8 ~" @1 H4 R3 B5 _消可交换半群& Z9 W8 C7 m3 ]
可消半群
0 [' H2 H) `6 k# s+ W8 p6 }& J可消半群2 s, T/ f* w7 C2 O: G8 v: E
消residuated格; \+ i3 }  W) z% t# @) Z9 S/ u
分类
& X$ l2 z( g& {$ X; N! M链
* ], V; Y0 e& |# ^( Y克利福德半群; G: C2 i- ]4 [6 t3 u& A; s- B
Clifford代数- ?" s3 Q1 x+ Z
封闭代数
4 h4 q6 G& [7 U" P: o$ G7 a可交换BCK -代数; ~! ^. b9 s2 y4 h% Y6 p- t  Y
交换binars，有限的可交换binars，与身份，零，身份和零
  x4 C9 r9 [+ L! k可交换的组成下令半群，有限可交换积分下令半群
! Q- ?" s! G/ k. z$ z$ Y/ j交换逆半群
, R! d# a, Y! W, Z3 r8 h2 T0 k交换点阵有序的半群
& ?9 F" E7 e2 C3 X2 K/ D1 u交换格序环
3 I8 W' Y; F2 u! o+ d  c: ~" f交换格序半群0 L0 T1 j( o) b  W# g% g2 Y
交换半群，有限可交换半群，零的有限可交换半群
, J1 C* ?3 a, ~. m7 P  v) V! K交换下令半群. A$ T3 u& Y/ I1 v5 ?! j
交换下令戒指
$ z+ U. t) K2 q0 V$ t3 y8 x9 P有限交换交换序半群，序半群
. S7 V. M/ W  ?" B3 i" i) A可交换部分有序的半群
; X  }) p. ~' M/ |" S9 X可交换部分序半群
2 H0 H3 a, ^! |( M/ C交换正则环0 L( I- P, P0 D
交换剩余格序半群
: D  C4 A/ r9 a7 i7 D交换residuated格
- O2 ?! k5 q* |6 ^' |; }  U可交换residuated偏序半群
+ A' q1 {* r6 F- ?6 P. A可交换residuated偏序半群
2 e! W9 ]6 T, ~/ z交换环$ u5 {8 d; ?4 r4 b0 K, F5 f: T1 ]
与身份的交换环  i4 d9 |. S/ }
交换半群，有限可交换半群，零
. x  K' |+ V' Z; ?紧凑型拓扑空间2 |) _: r) w7 _  s. @2 Q- _
紧凑的零维的Hausdorff空间
( k, q! p( N2 n5 U! x4 l$ A补充晶格; s. O  Q; P" C5 Z% h. V
有补分配格
8 f" ~; q0 f3 y8 H  m( {补充模块化晶格) E) n" k/ X4 d/ `, n) z( s
完整的分配格& n$ B# t  v. m' f, n& j* L# I4 g
完备格1 ^; U, j* z6 g
完整的半格2 k$ m, O8 a% \3 j
完成部分订单
1 y2 T5 w; c. p3 A' e完全正则豪斯多夫空间( Q: }/ d$ R. \1 C- }$ ~$ M
完全正则半群7 e/ J& C9 O* e
连续格8 _" o% {& n+ }
连续偏序集4 K6 s8 n% w& n
柱形代数. O; e, U& e% ~& f# B: x* Y% W2 U
德摩根代数
: l, a2 D7 C+ _德摩半群
0 p9 M) M& F; Q$ ]- `戴德金类别
( D, U! V- S4 n: g: H4 Z戴德金域
7 Z. n' a( _# {& t# ?( A稠密线性订单8 f6 _; c, E; w* F" O4 u" z# C
有向图代数/ ~. _& N7 m) \; B/ b% ^
导演完成的部分订单* J6 e& A  U; G' D% Y
导演部分订单+ F/ D9 N' j! d) D& Y6 c
有向图& e+ D3 W+ q" L
Directoids
4 {9 ~1 U8 s4 p& S& A分配寓言$ O) i7 O. m$ D) o- i
分配的双p -代数9 A' m; ~, Y' T5 G; c3 ~1 O
分配的双P -代数) R+ _6 w( M$ `& d
分配格扩展4 }* B* Z. E  V- ~
分配格
! D) u  `! B0 l( n4 A- ]2 t. l; ]. i( X与运营商分配格
$ c: e1 d0 {  O$ y3 _分配格序半群
; e; I) d7 L5 l' O- @# N分配p -代数
" H  \5 v" r, t; v" \分配residuated格/ m# f) [3 S' d# E' Z
司代数0 `( U6 m) o% G# U" k
科环6 z( l' o1 Q; v
双Stone代数
1 N0 J) ^& F; t- r" G邓恩半群, b0 _. l1 @2 w, m1 ^9 x
动态代数" W: C4 p3 V, R; }4 s: e
熵groupoids2 Y$ J: A2 h; W3 t
等价代数
' O* P9 K7 k4 V) Y" \3 b! V& B等价关系
3 B" C5 k% S, _欧几里德域6 X" a0 r9 \/ U' Z
F -环) f6 }; y, f& _; T% u
字段
( }( o9 N* k  v% w% g: o, C4 yFL -代数
% S# O1 D% _2 S9 c! AFLC -代数. Z3 A$ r3 Q1 v2 L
FLE -代数9 I3 V/ i1 y* g5 a& d: T
飞到-代数
7 Y0 l' h4 ~# `- A' m: Q- y6 s# uFLW -代数) F- r. O: L3 k1 R3 `) g
框架: R) \- g. u6 h
功能戒指
  q% V# w, Z4 u4 G( kG - 组) C, C. u; k) a* |  E: B
广义BL -代数
( G; e0 X6 Q; t8 @; ]. B: r广义布尔代数
( _7 w) L  j( \3 C  L广义的MV -代数2 T( q5 `! {& E( U: d  X7 o
Goedel代数
! m! C& q/ F2 w1 e图
8 \- a- B" \# oGroupoids- u/ o( f% M7 [2 b( k6 L2 n
组$ q" M7 X9 X) a- [  ]$ m; e2 E
豪斯多夫空间: F, Y+ I/ U& q4 Q6 c
Heyting代数
. E) k. |. }! V/ \# A$ J" p希尔伯特代数3 F1 k; D7 i1 E4 N% O
Hilbert空间: ]) n4 N1 @7 r& z, N; m
篮球7 G9 R$ O9 f* C0 o: ?
幂等半环
9 q/ I' H/ A% L3 O; T' ]! D幂等半环与身份
9 y% ?9 e' `9 ~9 M2 G7 j/ e幂等半环的身份和零% ?! c5 N4 y' g6 ^( I3 g
幂等半环与零' v9 _* M0 V9 T" m! T) _) p7 N9 D% o
蕴涵代数5 `/ c) r0 I6 O5 f) E; `
含蓄的格子* L1 d, F0 V8 R( H
积分域( f9 q6 x. c+ O( d8 G  A) v0 D
积分下令半群，有限积分下令半群7 i# h# f0 ]: h* r% d
积分关系代数
% G& {+ i) }+ R" `' |集成剩余格1 ~) |5 ^& [8 q( i1 H
直觉线性逻辑代数
6 t: y3 g* A; W- K& B1 i逆半群
6 [) b, h% ?; D, `合的格子5 r) K5 z! P/ j  D' v4 t
合的residuated格
1 Y  W) I! |5 u! `4 j5 h& g1 M% n加盟semidistributive格
! q& Q+ L" c# p: S+ Y加盟半格
5 d% E% Y/ f2 e# G. [5 V0 S约旦代数% w- M* D2 a4 j
克莱尼代数; n9 J6 }+ `7 n" u" h
克莱尼晶格8 c5 O1 B6 r/ l- Q& |7 ]
Lambek代数- X' |, Z3 K4 V8 M* z* @1 B
格序群
7 }; i' [- d, D8 T格子下令半群
6 @0 N/ G. c8 ?9 _0 ?+ B格序环0 |0 s" K6 }0 w' L
格序半群
! Y( J. w# t# ]7 @% q3 r栅5 w( x! [' {- N) q! `
左可消半群
) o, P" B, a& D( Z李代数7 K( d; O& R# o1 L. L% |
线性Heyting代数
3 A, ]9 n0 z6 L1 |9 F) g线性逻辑代数
8 H# d0 x: x3 @线性订单8 ]6 S+ \1 G" r2 q+ ~5 ]9 e0 G) O* o
语言环境
9 Q0 R" h* K' [: ^! N! o局部紧拓扑空间
3 w$ p) n" u# K- G循环
/ U' r0 f* N6 gn阶Lukasiewicz代数+ Q* q0 ^7 ^: t$ v6 [# V3 r; r
M -组$ Y+ p( l+ v- N% o% _' {) ^! E
内侧groupoids# |: L9 O, r) T% g
内侧quasigroups$ j- A7 ?; ^7 v$ r
会见semidistributive格
# ]( n# t* v- [会见半格
4 C) ]: }; {3 I. D; s) v% I0 D% G度量空间
) A% j5 H8 Y4 S* i5 P  H% @模态代数
, j7 S: d$ j7 p, u模块化晶格, F- ?5 o& |. f& J% p. z+ W( o  l
模块化ortholattices! r* F; b  Y) u5 [9 `
环比一个模块4 w$ a7 K. O/ P. E# m
单子代数0 N/ y( G* x7 M% J
Monoidal t -模的逻辑代数/ y5 \6 W' e& Y  p% K" u
幺半群，有限半群，零
9 E) d) m4 S& X/ d* w) Y6 dMoufang循环
' p+ `% t& J- o! ~, V- WMoufang quasigroups  `' T* |( e. z6 e7 A. l
乘添加剂的线性逻辑代数: W0 L6 }; Z9 m! j' Y. v$ N
乘晶格* f  ^% C8 z" X  |$ F3 x
乘法半格
" l& H4 X% ]" w# p" y! `多重集5 }/ {/ G5 Z1 R1 b; O# |
MV -代数+ u. _, |' Q$ e, m  O$ Z7 J
Neardistributive晶格8 N1 n9 Y' _, K* n! B
近环6 f) P! x7 d4 A1 m! i" U
近环与身份! R9 K1 O: n! h( T+ N6 ?
近田3 _3 w$ c1 S% _5 G: g& C
幂零群
, B& t; b/ x* x( G3 i$ @. s# \非结合的关系代数3 g% c( O# A& o& j$ |
非结合代数5 B# [1 q8 ~* Z3 Y" N( ]  l" x* r
普通频段, s2 Z% n% l; `) O0 c3 r
正常价值格序群
/ e% s" l% x% r赋范向量空间
2 O6 Z8 w8 {: k6 b9 @9 f奥康代数# p; y( f  z' l" r9 V. I( j
订购代数" |: `+ X! s+ H
有序阿贝尔群$ A4 G+ d+ M; B: T, J! W- t
有序领域  q2 ?( R* X: @4 i+ y
序群( l( M9 a; a) ~8 M2 C% [
有序半群
& B- T! b0 ~* M3 M' d1 R与零有序的半群1 h. e  @" R/ m
有序环
# [( h: O# n+ T5 T% J( [" K9 h$ F序半群，有限序半群，有限下令零半群4 y' l* _1 P! r
有序半格，有限下令半格! I' p  {; Y( u8 b; I+ r
有序集
% q/ n5 i- Q1 j# ^( ]矿石域
, A0 {2 e- Y2 [. N& n* WOrtholattices
" e$ w5 M# w9 P9 w, q正交模格: s# j9 j$ b  V; G- v6 F
p -群: o5 Z: _+ H0 ~, M+ D* [& y8 o
部分groupoids% j1 R  Y, O; x3 G! y# U6 Z
部分半群
  t% n" f, t' x9 @6 ^部分有序的群体, g$ H# ~! o5 k7 Z
部分下令半群
8 {2 ^) r; N; k0 B( n' b部分序半群- F6 [/ K( _$ ?
部分有序集" q- k# N  Y* {0 g2 v8 u5 K
皮尔斯代数% s) f" R7 N0 c# K  @+ b4 v
Pocrims& u, O% v1 ~8 }6 g. ?# b. Y/ E( @
指出residuated格
6 b5 N) ?, j# ?" n/ C5 J7 H5 aPolrims3 X$ T; k* y! J+ T
Polyadic代数* c% z" I% J( a, C3 M- A3 p1 y
偏序集9 F& g+ L" c2 @/ v& @+ i4 R
邮政代数8 j2 X/ @# i% q. e8 e
Preordered套) G( _; p# o7 f( _
普里斯特利空间
1 B3 l4 U5 r2 S3 @主理想域& l  D% s8 A! z
进程代数; _0 [* V# B0 [! z  t7 `
伪基本逻辑代数
: R1 K+ C" X) e& b/ ~* T伪MTL -代数2 T! l4 f# R( W8 U( ^9 [
伪MV -代数0 a. \8 O( ]/ E" {2 j$ D
Pseudocomplemented分配格- P  L7 X1 @2 N4 p5 s
纯鉴别代数
8 q' N  V0 i7 N8 uQuantales
8 O2 X- F+ I! V; b0 e" B3 |Quasigroups
% Y6 ~) c$ G. B8 L1 d准蕴涵代数
' d, z) m: m, M0 j准MV -代数
3 ]: D  j4 e: A) g准有序集
  O6 Y: e. ^9 f6 |Quasitrivial groupoids
+ b$ b" O2 O# u  }矩形条带
1 s- Z' D/ ?* V- R/ x自反关系5 F" e0 N5 e. i0 v/ o7 j
正则环
' }$ ]7 L) ^2 W. w% L! |正则半群
' Y7 r1 j" ]# P3 i- [( Z关系代数3 k2 K7 ^" y& _% C1 M9 n% |" s4 F
相对Stone代数: ^$ R6 L) S- S) E8 ?6 b% p% G
相对化的关系代数4 y5 p  c2 ?$ l
表示的圆柱代数
  A* W. {$ F$ e; M表示的格序群体
2 ?0 o; Y" x$ U5 G+ o表示的关系代数
' g: V7 r. x, U6 S; n3 a表示的residuated格3 F! q; H1 [; h: _  a
Residuated幂等半环
. q; _1 [) V% y3 g, x4 x剩余格序半群
4 q5 s, O  g. ^% W: `9 N/ `; l4 G剩余格
+ k% [% Y2 b: @$ H5 {  ~5 w2 v: gResiduated部分有序的半群  s8 v* O4 G' ^) b3 E
Residuated部分序半群
' z. K; g1 _; t; ~+ \+ u8 C戒指
& p2 d1 M& a6 t% m2 B0 b7 p1 r戒指与身份% a% ]' j1 U$ {1 s
施罗德类别
8 c3 N+ t% X, X* [1 ?  }2 H, lSemiassociative关系代数7 I. u' Y2 g" k! s: z9 t
Semidistributive晶格
* n! }9 [1 X) |: F7 q& Z5 F半群，有限半群# \* W1 D$ b* T% ?6 C# y4 B
半群与身份, o. X& K* V" l  a2 \' G1 _2 \
半群与零，有限半群与零
- U. p( \# Q6 x2 i9 _7 T- z半格，有限半格& ^( @: `& `6 M  \
与身份，与身份的有限半格半格( q% T9 e: _/ @! z# Q, o/ g
半格与零. B2 P+ s7 Q1 w- w: h  m
半环3 t/ B' W) u8 w; }' j
半环与身份5 G# _; g# U) F( P! A
半环与身份和零
4 \" J0 P. n8 ?% N. Z半环与零) ?) b1 ]$ F+ u# j  W& E( z
连续代数, |9 m7 V7 U7 K3 o# Y
集
$ G9 Y. B! M' o2 e4 ^, f1 q+ T壳
! x; H* g2 Z( I5 s歪斜领域6 k# s4 u! Q' h6 w+ Y1 a1 U
Skew_lattices/ f( b" ?+ @3 B3 A6 {6 \! V% M
小类8 k7 {( R1 o8 F+ T: L: |
清醒T0 -空间
# e) [5 A8 I7 d" o0 f- U可解群9 p1 n: X. e( q/ n7 d4 x2 P. `" _& K
SQRT准MV -代数
0 w( J3 Z1 b- B' Y' u$ S0 @, f稳定紧凑的空间7 ]. f$ m1 c* l9 A# ~
施泰纳quasigroups
& j. i, G$ t2 s6 KStone代数
0 n1 H6 P/ Y$ D  Z对称关系) X# b7 p" R) `% U, C
T0 -空间7 }8 \  w3 }6 v/ x$ A8 U; I
T1 -空间! o3 K& o6 e4 }, M1 Q
T2 -空间% i+ ^: z4 R  X- F& y. T" h
塔斯基代数
* I1 `& X$ v/ r4 v  S紧张代数3 }/ Z5 R' k# r, j, a) O0 n
时空代数
# ?* S- E# ~/ c2 `! B拓扑群* K1 ]$ j5 R7 Q( \2 G8 m8 f
拓扑空间8 t: f% D. Y: U8 a( a
拓扑向量空间
& b7 g) Y' a. g* V扭转组2 z2 i  s5 e2 v7 k4 u
全序的阿贝尔群
. M; W7 C+ X" p+ k/ O& L# k全序的群体+ l9 u/ m- l4 K. H+ O
完全下令半群
+ I5 K$ s3 m! A5 U* W/ f+ f; xTransitive的关系
% G- a) I( X/ W! x  u# {6 Z0 [9 a树
9 l/ u6 N! l7 V0 {锦标赛
7 V3 j  A5 Q0 M7 b一元代数; h9 {( j" {( U' S9 R- T+ D: N' T
唯一分解域$ B4 o( g/ L7 i& B9 U9 O& D. \! g
Unital环
4 b6 F7 u9 N( J& Q7 x向量空间
3 J9 E6 `# i( b5 }0 }. [4 rWajsberg代数
+ e# X; s# F7 g5 i# AWajsberg箍
8 T& d  c1 F7 Y' e& |# _$ h弱关联格
* c* N0 i0 j7 [9 R7 A弱关联关系代数
9 ?# _/ F' e0 j, \( ]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