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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

" O4 L+ y) Z; L. f* _; X9 j, w, O0 }
Abelian groups     Abelian group; \! t6 o# O0 e
Abelian lattice-ordered groups
& b+ `1 h5 C  ^Abelian ordered groups) Q: [- r' n3 o& Z' Y
Abelian p-groups
  T: {* Q6 P6 L" {- l1 Y6 u4 EAbelian partially ordered groups
( K; R0 c/ L1 t6 QAction algebras     Action algebra" d# W- J4 T7 I2 V  |' J1 @
Action lattices' K0 f$ C5 z8 N; c7 u. B
Algebraic lattices$ T  x2 O$ N% m) l$ R
Algebraic posets     Algebraic poset1 U0 w7 J: B2 q5 {
Algebraic semilattices
4 J- P; X/ K- m, G+ O8 QAllegories     Allegory (category theory)
& C1 L2 H6 [5 @Almost distributive lattices+ d5 D6 o; C3 W8 {9 |
Associative algebras     Associative algebra9 y& z  x- ]" c, P4 t" s+ H3 `
Banach spaces     Banach space, K2 g) O1 M6 a5 F+ a6 |
Bands     Band (mathematics), Finite bands
: {" _4 h0 r0 R8 a% s- e" a* [Basic logic algebras
* A2 q, v; I) O$ k9 r9 }& ZBCI-algebras     BCI algebra
  I6 _0 Q% q) PBCK-algebras     BCK algebra
  d9 D+ |5 f$ \6 S8 P# ]) ^BCK-join-semilattices
$ I+ S4 u  H6 d/ ?# ^BCK-lattices
! R& a0 }; h3 p9 B  qBCK-meet-semilattices* D% g" X% ^/ K
Bilinear algebras2 q  U% g% j( w, T% S
BL-algebras
0 Z9 x0 ^6 q8 e/ U. pBinars, Finite binars, with identity, with zero, with identity and zero, ( H; ]3 g' o& I
Boolean algebras     Boolean algebra (structure)
9 _; O9 l9 o$ qBoolean algebras with operators# h+ w8 E) F2 d. _* `$ @( J
Boolean groups# s/ G. l+ a) U7 b8 q  V
Boolean lattices
! |4 }7 Y& ?- z5 DBoolean modules over a relation algebra* K5 N' G( E/ y0 a; b
Boolean monoids
6 Z# O8 T, ~% T3 u+ w  N" hBoolean rings9 d  k/ x9 H6 M1 _( E& o" \" n& ^
Boolean semigroups% _$ x8 [; e* N: E3 B
Boolean semilattices" x9 B" u$ E& b* h4 ?  n
Boolean spaces6 x+ @% x5 Y6 ~0 ^* b- H8 x, G
Bounded distributive lattices
9 e3 z, `4 Q5 m# SBounded lattices/ z+ h4 u7 o$ P  e
Bounded residuated lattices) y# s2 }' u( L+ `# `
Brouwerian algebras( H& ^) c3 s3 c; [% M
Brouwerian semilattices
. J- u1 b5 d1 p* w+ A) ?. OC*-algebras" p$ S1 y. e8 S: B& I6 f3 B0 T, P% F
Cancellative commutative monoids9 F  H% M4 D" q& L* [
Cancellative commutative semigroups
+ R% H8 S6 V, G4 tCancellative monoids
/ o; Z8 J! T7 g. b$ Z9 gCancellative semigroups
* l4 L0 u( d3 E+ t3 |: _$ DCancellative residuated lattices
9 N9 `* S, h+ o, UCategories
0 z6 ~. m+ l  P" ~Chains
' P# u1 i( i# D, X! X: TClifford semigroups
/ S; ^/ L+ ?+ t3 yClifford algebras8 i" J( [; j  V1 P% s6 d
Closure algebras
/ b9 H# h3 r9 }- iCommutative BCK-algebras+ J) n' [5 u, ~# r0 G2 ~
Commutative binars, Finite commutative binars, with identity, with zero, with identity and zero . l4 |2 S7 S% Q: {
commutative integral ordered monoids, finite commutative integral ordered monoids
9 s5 D. l! t' l6 ICommutative inverse semigroups
% [0 k+ n) ?* Z6 d" ECommutative lattice-ordered monoids
, `8 D1 q  G  U9 d3 ^Commutative lattice-ordered rings& E2 f$ S* r" G7 ~
Commutative lattice-ordered semigroups
# [7 [* J/ y: h/ e) Q7 s5 O" l3 ZCommutative monoids, Finite commutative monoids, Finite commutative monoids with zero
9 A  R; q( W( ~$ }! VCommutative ordered monoids% q% N. V# s8 z& ?
Commutative ordered rings
: e9 [; G2 t# X; a3 j/ I7 K% `Commutative ordered semigroups, Finite commutative ordered semigroups
' N( b- L; v6 [3 R7 @5 rCommutative partially ordered monoids7 f/ h7 Q+ A3 v! L0 s2 W
Commutative partially ordered semigroups
% {/ d4 O' D0 `$ V0 k; a7 c( ^Commutative regular rings3 n: V' g: _8 q3 k7 s
Commutative residuated lattice-ordered semigroups
7 ^5 y! {0 X/ b* g) ]Commutative residuated lattices
* e5 ~) \) s' `4 f- ^3 V0 |  @7 zCommutative residuated partially ordered monoids
4 `, p3 @( v3 A$ \Commutative residuated partially ordered semigroups
) D  N" n- h% s6 R' D* |' z& MCommutative rings
3 ?5 m* w0 ^- k3 v) uCommutative rings with identity) ^, a  [- A" A3 t
Commutative semigroups, Finite commutative semigroups, with zero/ \- \' A+ p# y
Compact topological spaces1 B, d: B! Q8 K
Compact zero-dimensional Hausdorff spaces
( E) h. c1 w8 ~  O0 m7 MComplemented lattices+ y% S" ~/ H# A* }) k0 H' U
Complemented distributive lattices
% k9 p. b/ T: t/ f9 j; I) FComplemented modular lattices
) c6 d. o+ L, a8 H  O; z- g* JComplete distributive lattices: A$ Q6 k" V2 A2 y' P! e
Complete lattices% |9 U! x- ?7 m
Complete semilattices
9 n, ~# `/ G6 l- _9 }2 H  WComplete partial orders7 Q( _. y% t8 J6 W. H8 E
Completely regular Hausdorff spaces, S3 A/ L4 ?6 A4 V
Completely regular semigroups) s0 o* B0 d5 g( v9 ^# @: E( g% F
Continuous lattices8 j7 H: B& \9 g" {/ o7 K
Continuous posets
" _' D3 v1 B) s! v  ?) H5 t. ECylindric algebras
" @  a5 N, u' g/ R' A# wDe Morgan algebras
$ J3 K: N8 \  KDe Morgan monoids% U2 N9 U" q, p3 _
Dedekind categories$ o  D, j6 ~9 F  l4 _' N$ _; Y( s7 m
Dedekind domains% m: z5 \$ u* @* N! N% Y" ]3 v
Dense linear orders/ n! `8 J/ p1 Z- A+ f
Digraph algebras' d3 k  c+ `  T4 A" N* _1 ~
Directed complete partial orders
3 w- f6 n$ V' _5 \) u$ GDirected partial orders4 J) q& u/ r3 [  n# C
Directed graphs+ h4 k- S! v0 P& H6 Y) h
Directoids8 Y' t' ?. i3 E% j* }1 k- G) U
Distributive allegories, H' G5 v0 X4 I- @! B
Distributive double p-algebras
$ c) s" W0 G& b/ MDistributive dual p-algebras
  x, m! r9 Y6 T& `2 B+ ZDistributive lattice expansions
% J  N: t$ Z7 D4 j7 c% SDistributive lattices
& U( B# l. M  N4 r, E+ VDistributive lattices with operators
! C8 b! ]% ~% {( }: Q' i0 ^Distributive lattice ordered semigroups
' X7 W0 \/ C+ }$ |2 g: dDistributive p-algebras& [2 ]3 Q5 B# s7 _) z' y) d( N
Distributive residuated lattices' n6 ^: k5 B% `
Division algebras
) [6 m/ n1 z1 D5 V$ D& `2 iDivision rings/ U1 w  I$ H# y
Double Stone algebras
- B/ {9 l2 Z# k5 h% FDunn monoids
( j' ^3 V* u/ K$ ^- h3 UDynamic algebras" X1 `- V2 B: `: U  N. Q# {( [' _. @
Entropic groupoids& X, I: E( z6 d- S$ j9 q+ g
Equivalence algebras
& h8 `; o( `* t/ g: Q- h3 }% a) uEquivalence relations7 U' T3 v$ a9 e! K; H
Euclidean domains7 \! U# {. }- n  T" J
f-rings
3 |1 ]) y) r- N9 m, A& U! B. w( _Fields
/ j; h* Y: [/ k+ T& VFL-algebras4 ?6 s# h3 s0 I' L* ]0 G
FLc-algebras
' n6 {% |7 e1 @/ w+ XFLe-algebras0 h! i  d4 o+ x( ]3 i# e% ]
FLew-algebras
% A5 s2 O5 m$ x- G) g0 RFLw-algebras9 w) A# t6 |. f. k9 x
Frames! y: E; ~: |- S1 I
Function rings
1 @. K. _1 j# d: mG-sets) l3 v9 F' t3 e( Q9 B3 ~. R
Generalized BL-algebras, \2 |" [4 G& i, ^9 a% \2 ^5 N2 e9 O
Generalized Boolean algebras. j: W7 i. m' y2 e0 v) i! R
Generalized MV-algebras0 {0 |3 ^! p3 i! Z% n5 I
Goedel algebras
, G1 c  ^+ n6 y% C, `2 H* `! MGraphs8 I8 @, d, C/ p" s" x2 \0 Q! V
Groupoids1 R: k6 z0 ^( e3 Y
Groups5 {; x: B9 c0 f# e4 L
Hausdorff spaces
# ?4 d; @" {" o( o2 r5 KHeyting algebras- U( ]8 X6 @5 I  q5 ]
Hilbert algebras
9 W9 n1 W; A% C2 W, T; J! eHilbert spaces. c) M, I3 k5 v6 y% Q
Hoops% t3 i7 t- A7 i1 `
Idempotent semirings( ^) }: R$ i: N! z. Z, \4 _
Idempotent semirings with identity
( Y5 o8 L5 n. h! e% k$ k/ MIdempotent semirings with identity and zero
; G$ @& Y# [$ j9 `1 SIdempotent semirings with zero
. o4 E' m: j! K4 {: I1 ^Implication algebras
* Q; Y" G- h$ m  v: Y$ R4 t2 KImplicative lattices
6 V, [5 @3 Y9 X$ |$ M4 L# A, CIntegral domains" q' k- S4 p+ a0 F; R5 c9 [
Integral ordered monoids, finite integral ordered monoids
9 C$ h4 d, X7 O( G* a3 m3 q; ]Integral relation algebras
3 I* |/ G2 s1 M/ W7 {4 _Integral residuated lattices
) m* S! i2 r, u2 H+ ]# `" m4 p/ C; sIntuitionistic linear logic algebras6 I  i& {2 F6 b+ X5 K; z
Inverse semigroups
7 Z- a! E2 l3 m# P' N2 XInvolutive lattices( ^7 l( M- j0 ~4 U) A, O
Involutive residuated lattices6 G, {3 C; O: k
Join-semidistributive lattices
$ d2 w. j& x% a/ v+ w/ M& n+ O# o) z2 hJoin-semilattices$ f5 O- _7 l4 f4 `% x7 D+ \
Jordan algebras5 b, ^1 v6 U" A4 ~5 ]
Kleene algebras
0 I% l0 z3 [9 _' U3 k$ d, w) |Kleene lattices
* e" b7 m) D! mLambek algebras
) Y3 K" J1 a1 A; H& DLattice-ordered groups: k( T$ U3 i4 w: w( o3 [$ \6 [
Lattice-ordered monoids
* @1 V) h" `7 X0 l9 B: Q+ q8 }Lattice-ordered rings
- k5 D" P. D! U5 HLattice-ordered semigroups' j6 c% H$ h* ?/ U$ Q4 V! H
Lattices
6 e, @* ]  h. E: C# BLeft cancellative semigroups( {1 `3 |- z6 F- P  b3 ~% ^
Lie algebras; t8 L2 R0 X& b: x4 x6 m! \7 b/ b
Linear Heyting algebras
' s1 n0 R4 q7 ]: q' a6 i5 WLinear logic algebras* B4 B) l: k/ q+ o. ^9 d
Linear orders
4 S1 p- T2 r0 j0 Y/ L! h! p; I' q" J8 wLocales7 J9 H0 h5 x& D
Locally compact topological spaces
; Z9 z3 {- ]; C* q' ]8 {Loops# g! J% _$ q; H9 ]/ f: x4 `: ~+ h
Lukasiewicz algebras of order n8 Q9 v7 I, o( }/ I$ K
M-sets. |4 n8 r1 c. T4 f+ I# F
Medial groupoids$ K! s# m& G; J0 k
Medial quasigroups. W5 `1 }% V: L0 X' R& N4 T
Meet-semidistributive lattices
; L0 G; C4 R& Q" b- zMeet-semilattices) K, `" ^* f2 N5 g; D! k( U; _% B
Metric spaces8 r- x( H2 C. l- y! X9 q6 z
Modal algebras6 h' \: j% Z6 {) y
Modular lattices# \- ~8 y- f4 ?8 a7 ~
Modular ortholattices8 B0 B, z3 O5 R2 I; t' v
Modules over a ring" Y& G/ ~) w- {4 o5 k7 |$ M
Monadic algebras2 h+ W' e( ]7 K$ x; ^
Monoidal t-norm logic algebras
. B5 F6 N8 N( c5 g( @Monoids, Finite monoids, with zero! Q2 N4 Y' u6 m6 f8 f& d- c% R
Moufang loops4 i2 ?8 ~2 t5 T- x, ]7 ?* K1 x5 ~
Moufang quasigroups* l8 \- \* |7 Y, @  g
Multiplicative additive linear logic algebras* x: @9 L3 [- f" |% R" z, @0 S
Multiplicative lattices
3 p' r) F# R! V/ LMultiplicative semilattices
9 c# `' a5 B" K4 m% i5 W5 SMultisets
% M7 x5 {  g1 C, pMV-algebras
' _& ~" H4 ]0 b9 F6 T* D" z, xNeardistributive lattices
8 q( k) |! O0 \6 Z0 A" m/ h6 y( BNear-rings7 S& M  y& k# w! }2 w+ |) i
Near-rings with identity6 {3 [/ C' b; D/ N- R. H  `
Near-fields+ J( ~' m) h5 D
Nilpotent groups
- A! H6 d( T% L1 {" H% [Nonassociative relation algebras: m7 `% K* |& a0 k5 X: p! M
Nonassociative algebras: X  `) m2 G( G9 o: }6 I+ p' O- Z1 V
Normal bands
3 A2 Q' Q% F8 ]5 y5 H) m. sNormal valued lattice-ordered groups
& {/ W, G7 O! J: sNormed vector spaces
( P" f; S* z/ i5 I. S3 Z9 ?4 qOckham algebras; }, s( C5 E7 K& t& L  i  D& j
Order algebras
+ R% t: h! F9 U# ^8 l' F3 fOrdered abelian groups" b: v% |$ r% Z
Ordered fields. p3 ~- ^7 K3 N! O! Y. z' A9 B. y+ j
Ordered groups6 Y  K, b/ r$ u6 K$ m
Ordered monoids1 v2 g/ F; z% {& b4 v
Ordered monoids with zero/ S6 B$ o: ?. [' @
Ordered rings- N3 ?( ], m- v! V
Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero+ V& H* @7 T) v. }' s) A4 e$ A
Ordered semilattices, Finite ordered semilattices
( e- z8 M* g! M# A* L, B9 T& uOrdered sets
& k- f& v) `5 \4 c3 mOre domains
. ?, O2 Y& n& OOrtholattices! \$ U& e5 V. E; h6 L
Orthomodular lattices
2 [4 B# R$ e2 w5 p* Z4 Z% n8 q+ kp-groups0 X" x  `3 V- I! R( U" u5 P
Partial groupoids
; k* z7 S5 o* l7 }7 O: xPartial semigroups
- J' w, c6 g6 M. w2 t* q2 v  wPartially ordered groups
. g# G, m0 G2 n% W+ p9 UPartially ordered monoids
" a# S( T/ ?9 X0 NPartially ordered semigroups& _" S0 J6 y! O
Partially ordered sets
: d9 N% }' ~6 S0 J$ r/ k8 OPeirce algebras
0 G) ^  c9 I4 Z% APocrims& u% y4 q( R  e- O5 \1 x
Pointed residuated lattices
( Y) @, {& N7 q' a' cPolrims. ]1 k+ h% z: k+ i7 Q9 N
Polyadic algebras
1 T! T! M9 T+ aPosets" S( w$ Z9 _7 _3 N) I( x
Post algebras, e5 `' u' {# Y8 q. ~
Preordered sets3 h! [4 t2 t$ o0 [0 d! t% [3 u
Priestley spaces& v$ Z8 q7 ~0 u
Principal Ideal Domains
( K( `" ]* m! S* [( @3 ^Process algebras
/ o/ H9 s) m- h1 L) U" \4 r0 l- QPseudo basic logic algebras, C% V5 ~' `* E3 R7 T( O  e3 |
Pseudo MTL-algebras. x; ]" ?& X5 y8 d. D
Pseudo MV-algebras7 M  Z5 f+ r; d2 a
Pseudocomplemented distributive lattices
# O" b4 v# r5 l6 s! YPure discriminator algebras- O2 G, F7 i% w* ~
Quantales6 {: y3 C$ s$ |1 p, K
Quasigroups8 G: @9 |4 Q. A3 e/ y! X0 c
Quasi-implication algebras' m2 J8 O& a- l6 w( {) t2 C  g  M
Quasi-MV-algebra2 k: a* o% M0 ~, U; C6 X
Quasi-ordered sets
" e8 ]3 ?. w$ C6 q" W% T: }2 eQuasitrivial groupoids7 W1 b  X% p7 A* K# h5 Y
Rectangular bands
! H/ G- G; N$ U5 q0 DReflexive relations
9 y3 }0 |) r2 r/ M* KRegular rings4 Y( U  u9 c  u, z8 O( q' u
Regular semigroups: A' ^$ s6 ]" w. k4 r/ w
Relation algebras
0 l. f5 k& C( E8 T+ j5 X! B4 ~Relative Stone algebras
2 E; n6 M% z6 FRelativized relation algebras
- C' f# O& u- }Representable cylindric algebras
! z! D) ?( a- h# {& r" o. W* CRepresentable lattice-ordered groups) s- h9 W4 K& d( @( T
Representable relation algebras6 A0 Q4 r: k' o2 Q  _. T  s; P- y
Representable residuated lattices
2 k$ i& n/ X  |1 z6 `8 z* yResiduated idempotent semirings1 B. @- J- g$ t5 v& c) [
Residuated lattice-ordered semigroups: C. S  r  s& J6 y" m6 u
Residuated lattices2 D/ @  ^, K2 p3 W; Y
Residuated partially ordered monoids
! f- `( ~9 K4 |8 t6 M0 J+ \) c, W, LResiduated partially ordered semigroups; l) d8 T3 H- h: H
Rings
6 {( U7 C( s7 DRings with identity. l6 n' U2 y- q
Schroeder categories
1 S+ D9 A: [4 cSemiassociative relation algebras: h. [/ Z- q0 @8 g
Semidistributive lattices- V. k2 z( C) F: T6 M* \
Semigroups, Finite semigroups
6 ^" m# I# k* C  DSemigroups with identity
! p. e. n- p* J" {, {- z  z6 ZSemigroups with zero, Finite semigroups with zero
1 n) w5 H0 W" [Semilattices, Finite semilattices) o2 U( ^5 w4 b; |, s. x) ?" ~
Semilattices with identity, Finite semilattices with identity
: j# R8 R3 U2 |/ r% VSemilattices with zero
' |" D0 H$ u5 v' pSemirings
& g& l5 ~" J6 k7 ?Semirings with identity2 o$ U: E$ I* r8 j& `1 _; l1 L: Y' `
Semirings with identity and zero
8 F: i4 c7 w* g9 g5 f0 A5 K/ E  c5 HSemirings with zero! n, K3 B7 M; i+ g! ]+ z
Sequential algebras
5 U) k+ k4 t& P6 H9 T. t: ESets
' O& I# I; L" e% p" i% oShells
2 M1 a/ I) m% X7 hSkew-fields8 y5 z% L- n( c7 [8 y
Skew_lattices# J1 {7 X5 |1 A7 e( M: I
Small categories
/ E+ S7 d5 Z; f3 \# v- P$ [Sober T0-spaces% e0 H+ m0 ?; V& `; i; c  A. |
Solvable groups
5 T) R8 d% J9 P% S" JSqrt-quasi-MV-algebras! M4 @; [/ r+ i1 X1 O* a
Stably compact spaces8 g, B8 R/ y& I
Steiner quasigroups6 O) _' A+ m( _% O) G
Stone algebras
  O0 [0 ]! [9 ~$ ~Symmetric relations& Q& }$ `2 Y; {/ K$ f8 N
T0-spaces' g# O" y" Q3 I/ h* Q
T1-spaces
. A2 J  ^; S8 N0 rT2-spaces
8 w, @3 }3 h0 J* wTarski algebras) c8 M& `  l& N1 K( m& t" S  x
Tense algebras
. w' s6 J, U/ {Temporal algebras, Y! Y$ G# k. K9 T: G/ A' k" v
Topological groups
* }6 ^. d  C6 p: o3 _Topological spaces5 m# k6 t* H% W) t' y
Topological vector spaces
  h  ?, W- C# W4 {4 dTorsion groups
' v8 |: c. G- e/ l' TTotally ordered abelian groups9 ?$ o5 f& z; b+ b, A8 t; j
Totally ordered groups8 \( Z! [% j/ h; n
Totally ordered monoids5 b% e7 P, `, B. G
Transitive relations
; p- M: ^1 F* b1 z6 }, c& T+ N) cTrees
, W- L8 Y) W9 _* ~$ [9 p" W  B! xTournaments# ?) }7 L, Q* |9 Z- Y
Unary algebras( X! f. v* U6 p6 y  I
Unique factorization domains& i: S1 o1 c4 I$ ?, r, a
Unital rings
9 n" o2 {% x2 iVector spaces( Y/ Q0 L% G" ^, N8 f6 V# Q
Wajsberg algebras( U/ _/ v3 ~% x2 o" L+ O
Wajsberg hoops
$ x; y5 q* ^2 u$ \- }- MWeakly associative lattices
& }: p. `2 a' M4 U7 C/ ZWeakly associative relation algebras9 I2 |8 r4 w8 _" z
Weakly representable relation algebras4 o" C7 s6 U- g9 `& P
作者: lilianjie    时间: 2012-1-12 13:20
阿贝尔群Abel群
2 G' s5 b' \% ]6 S$ d1 i$ f阿贝尔格序群( P: F- E& O! \$ D
阿贝尔下令组, }8 e. C2 d, h3 h/ t5 f( Q
阿贝尔p -群' [0 t  A5 W( a+ @
阿贝尔部分下令组& B' i" R- X7 j& u) r8 T
行动代数行动代数) A, i. t1 D9 z
行动晶格
+ {5 `! L) p8 V  d4 T" {4 D" q代数晶格
+ U7 F: w* z0 b3 }代数偏序代数偏序集
8 c' x6 ~" I6 M# f, ?代数半格
5 a$ J) F5 b  `1 M2 b寓言的寓言（范畴论）
- r& {% N! o3 w' N& ?* e6 f几乎分配格
5 i" H" P) C4 c: c关联代数关联代数3 R# R+ U6 c. G1 U. T& y
Banach空间的Banach空间3 P6 {, T/ Z4 Z' A
乐队乐队（数学），有限频带
1 A# u8 h  C) G1 j! s$ m基本逻辑代数1 M/ }" _) J) X
BCI -代数的BCI代数
2 x* u$ Z1 t! `+ N( y* @BCK -代数BCK代数
% C# R! w/ w) S$ nBCK联接，半格( C- y" y! J$ |8 f# X: \
BCK晶格3 `- l9 S1 u9 K( {
BCK -满足的半格8 v4 b; K/ y$ q
双线性代数3 S5 ]" Q, `- Q0 w
BL -代数9 l' f) H6 J& O! ?9 N4 U9 E
Binars，有限的binars，与身份，身份和零与零，
, {% V. S( K6 H* l$ n  A1 z& a3 D布尔代数布尔代数（结构）; W( V  H9 ]8 m! W
与运营商布尔代数
' Q0 U( c4 T$ u布尔组  J" J' R9 A& r  F- Y" e3 i8 T
布尔晶格
0 h# F0 {* B1 ~4 L对关系代数的布尔模块
' i9 \  U& p9 j* g) p, f布尔半群# F8 T+ n3 t% l- J  t
布尔环7 Z0 h! t) p- f$ ?  [& z
布尔半群. B% o- [) |$ }. s' x! g
布尔半格; z0 [" I5 v" t( l# c6 P( T0 D! n
布尔空间
5 ^* ~: g8 g& A8 P有界分配格
) _8 P+ h- h3 w3 @界晶格
( j$ p3 T, B" \- D/ D; ?界剩余格, V& u, J3 p+ N6 p
Brouwerian代数& v% g+ w9 @6 L6 c% Q
Brouwerian半格; g; f2 I2 }" ]2 S$ Z# V, D
C *-代数( G+ P0 N/ B: u5 A
消可交换半群/ b- |, b, V5 c
消可交换半群3 `$ u/ a. t( B9 O
可消半群4 X: L9 N6 U6 I  \; T; I
可消半群
- y4 u- a5 O8 [消residuated格# j4 d/ w' r, {! v- O
分类
1 J% c& P+ _; ?: n5 B8 H链6 v% O. G5 V9 Y& \" V( v
克利福德半群
$ J8 D& C2 B5 Z# t9 P" h. v* CClifford代数4 E& ^4 g9 N; u9 B
封闭代数
+ x. ^  [! [5 h" l可交换BCK -代数0 a2 T( ^' e+ q7 j, ~
交换binars，有限的可交换binars，与身份，零，身份和零0 Z4 L& u2 \2 S; }1 P  U+ p. j( T
可交换的组成下令半群，有限可交换积分下令半群; c* [/ e+ P$ e  R5 ^8 {% T9 f
交换逆半群
( L. c+ T- U0 E% z, I交换点阵有序的半群& m$ g( N3 i4 H# a% U, B/ u
交换格序环8 N2 A6 ~: `- K9 C  Q$ U
交换格序半群; e& h0 _$ W! l: h3 n
交换半群，有限可交换半群，零的有限可交换半群9 W) g" K$ f! G, t& u' C+ p3 V
交换下令半群
+ W4 r) f9 ]! B交换下令戒指$ f$ M8 f* u$ A4 j) N! ~" T
有限交换交换序半群，序半群
6 ~# U) e& g6 r+ L8 W0 p, ^可交换部分有序的半群7 t3 _; e6 {$ t# p* l
可交换部分序半群
; L" r4 j, _' N. m5 }交换正则环
9 z* b; H: @) t* ]# c, u" C交换剩余格序半群
7 r! A( L( T/ ~# }, L交换residuated格1 d* [2 @7 t$ o# P' ]/ U; o0 d
可交换residuated偏序半群# p: W) {$ `: [3 _* J/ q
可交换residuated偏序半群& Z( i3 X; D& W  S+ f* S
交换环8 D- ^$ k" m$ _8 J
与身份的交换环
& a! ^; e, _. Z( p9 G: q: D2 t+ o交换半群，有限可交换半群，零0 n& ~1 s: J- S  V9 ~
紧凑型拓扑空间% W8 i* j4 _- W9 O# z) X
紧凑的零维的Hausdorff空间, j5 k/ V, D+ o3 v
补充晶格  P. A3 Y% D5 d; X
有补分配格
* ^  ^5 A; J/ U1 _$ Q补充模块化晶格) ?: O5 A4 X* E5 d% ^, c+ P" m! ~$ |
完整的分配格
0 V4 T; W# M2 Q9 Z  j完备格
5 O  l/ H! r5 V8 G完整的半格# P" l: C6 O, w
完成部分订单( r/ E7 p3 k7 M# M
完全正则豪斯多夫空间
) _& u- l8 U* H: w3 Z% N完全正则半群
) C2 C4 j, _  |1 Y. v: A连续格
$ ?- Z5 C& F7 d  l! B& d: E& {$ K连续偏序集2 d2 }: ~+ n3 ~1 j6 u' r
柱形代数/ \! ]: L. @  e3 t  [& Q
德摩根代数
" K& C) I# Y  @德摩半群
% a4 P1 q) e7 O0 Q3 P( A戴德金类别! ?6 X0 [, j1 M' G( r# G3 }, ~
戴德金域. `+ p& w0 ?8 T5 c
稠密线性订单& D, m7 w" ?6 k8 U( q. d  h2 }
有向图代数
: a* c$ [+ q  y; s导演完成的部分订单
' U6 x0 w$ Y4 S2 Y. A- G导演部分订单
' e) S; `3 C+ U5 S% i' L5 X有向图& ?6 o; q' i8 p+ Z* z$ l
Directoids
) }; K9 R) B9 G' f5 e分配寓言" S$ \! ?2 r! T$ {5 |1 V$ O
分配的双p -代数
) ]& b* {8 h' d分配的双P -代数# i* A' M! _0 G& J" h) @; a
分配格扩展) w: C% V  o! {6 _, }  I& ~
分配格
" l2 G/ V. v* q, E与运营商分配格
& X; z! ?+ l% N& B. M" t分配格序半群
" I+ g" o3 h, v9 H& `分配p -代数& B) k1 ~9 A5 ~. U9 z" l6 a& _: m5 a
分配residuated格
/ o% l4 r. F" R" y+ Y1 f" ]0 W司代数1 E8 N% g; w1 u, R" x, [8 S
科环/ T$ m! I; I4 e# v# [3 ~* M
双Stone代数' ?3 V9 y  {; d2 L) t
邓恩半群8 R! |# g: `9 z( R# f
动态代数
% o) }: i/ `, u熵groupoids
; p/ i$ g7 {- A* [  Q2 k/ Z4 \8 g0 D等价代数
: C6 f7 z. e" y8 \  e等价关系
) C9 k& F8 @1 @: X$ k# R( s5 S- _欧几里德域) E. b" g& J! M  B
F -环
! `' z3 @5 X2 M) O' ]& |8 r字段9 z8 z1 O) T9 \1 T
FL -代数) D5 Z% X  O3 t
FLC -代数
6 o* {7 z$ @' d4 L' u; aFLE -代数
5 N( f5 y; z3 R1 z飞到-代数
7 q% l. p, m9 ~: PFLW -代数8 q7 e2 m* }6 x& S* N
框架
/ Z" `* L) _% G: O$ V$ \* _. U0 ^功能戒指
3 I) Y1 e( P7 w$ j: VG - 组: _: J( `2 w* ?0 L5 R7 \; I9 N3 ]' T* G- X* s
广义BL -代数
  R* A4 s3 \( [$ i广义布尔代数  r; }% p" V8 q; G, u& {5 P7 F* f4 V
广义的MV -代数+ q- h/ Q/ X$ a9 r2 \% D  O* j
Goedel代数
  _7 C) ?$ e1 d! R& U) _图1 l4 s/ f8 t3 D
Groupoids% ]' u+ Z& u' `% w
组
. O/ b+ U+ P: E4 g  W; j0 K豪斯多夫空间
& L6 O5 j+ N' _) R$ S7 qHeyting代数
$ h* t- r7 w% x希尔伯特代数5 d- g6 V4 L8 d
Hilbert空间
) P+ T( b) R- b5 H! Q& G' w" i篮球
/ Q; ~" A% W3 ?- W& |/ g幂等半环' X# U4 x, A; o( P4 t
幂等半环与身份
. t7 {% Q: Q/ K: X幂等半环的身份和零; e8 l, l8 {; V
幂等半环与零
- `" f% j; X. B蕴涵代数' k- Y/ w/ `/ g6 Z, ~0 r; A+ {
含蓄的格子$ s1 r$ v  S3 X/ K- p- y: w
积分域% o4 o9 y+ S; d
积分下令半群，有限积分下令半群+ e; o5 I( ~: G1 g
积分关系代数: p; ]: x: [3 O# H/ z. {: H
集成剩余格
! W  P$ D8 c4 [' q直觉线性逻辑代数
- x8 O5 p+ A0 M1 j1 k3 N逆半群
, y; B. S) g, |4 _$ s% `合的格子
" e' M+ a" `' R+ T; `合的residuated格
& x0 h2 O2 i" z5 K1 ^加盟semidistributive格
7 R4 c5 a) l5 @5 F加盟半格8 b8 F$ t# c1 |; ?! f' Z1 R
约旦代数+ M7 _! d2 L" ?! q( n0 \: z
克莱尼代数/ E/ E8 z) b, O$ O* a
克莱尼晶格- I+ x+ ]! Q* S2 i+ Y( I% c7 [
Lambek代数5 h  C) M9 `1 `, u  Q4 f
格序群
" c" V* f, w/ }4 Z: {9 x格子下令半群4 k# u3 M+ o! o% X. \  P
格序环3 c- [: e0 I9 `$ @
格序半群
9 t6 e. X1 p, P$ p+ j栅
7 w* |5 j4 O" q! {; M! k- s左可消半群* w5 @% U0 R0 }
李代数
# `9 J% b) o+ x4 P6 `! i6 j( `线性Heyting代数$ r6 G4 T$ |5 _. C& q* A* Y4 P
线性逻辑代数
/ k2 n: W/ Y' g! i# h1 d线性订单' x8 \6 b9 {2 `- J- Z* q
语言环境' |4 l) _' U7 l2 w% @
局部紧拓扑空间
) o( ~" U+ f$ r5 o$ \循环
( A, K( ^+ ^, ]" f7 Z+ Dn阶Lukasiewicz代数* x  u) i$ E- z4 [6 t1 s3 [
M -组+ [" E  S3 ^- ^0 ]4 j# z
内侧groupoids6 h7 y  p5 d- @  I7 R
内侧quasigroups
4 n# N/ q3 R& V, q% E& d  ]会见semidistributive格) V) t) u/ [' ^. L
会见半格" o; Y1 l! |2 }
度量空间" X. I8 L1 Z; E: c1 @2 b
模态代数
1 l/ W6 Z2 ^2 f4 D模块化晶格
8 Z$ I5 L% t. Y! Y! }模块化ortholattices2 W! {) l& x8 n7 L
环比一个模块
1 l2 M7 k  y  {9 [5 v$ M单子代数) \7 V: I5 ^, D2 P
Monoidal t -模的逻辑代数
; x, Q5 p6 V8 R幺半群，有限半群，零; {. A( o; B% h9 j* A6 P
Moufang循环
) J5 y; v# @+ H" IMoufang quasigroups4 H1 w3 i" W7 ~  g# o9 h# K
乘添加剂的线性逻辑代数  t- D6 w# \5 }/ m2 |! P
乘晶格
! Q7 V' i8 G' }0 @' d! H4 F( K9 n乘法半格
! V8 v: w: m- U& x多重集& E& q8 Y( D: Q: s& e
MV -代数
# n2 c1 a! m1 p9 Z+ dNeardistributive晶格
5 ?- G1 k4 C3 ~0 h近环
- t0 P" F/ B/ J; g' s$ L/ J- g近环与身份
9 w, b) r3 C$ p! J' N" ?+ @# ]+ G; `近田
& F2 }% _& Z2 x# n1 }幂零群" u' G1 F/ T% N
非结合的关系代数, `+ b6 F6 E4 ~& r; ]
非结合代数! V9 ?5 W% ^7 B2 ^" j3 y% {& J
普通频段8 ^" P/ ?- |5 E. @' h2 Z! G, z
正常价值格序群
  z! K- r, ?+ `8 A1 b赋范向量空间- ^  }9 N  j+ {- `2 ]  R, m
奥康代数  }' n# Y3 |, D" a: Q% \
订购代数" M4 d" m3 m& X5 n- V6 }; m% t
有序阿贝尔群
8 ^4 r5 P/ \$ O, Z/ }  ~有序领域! d0 N2 Q( h' \8 s3 T) v
序群+ P4 _: @# B0 A! z
有序半群" @$ i3 W$ `# P# v5 E
与零有序的半群5 [: y: f0 a2 a0 S/ m/ ^
有序环* t5 H. L# C! N5 o" b( @" o" q
序半群，有限序半群，有限下令零半群
. ^7 P/ X( W' e* t$ f/ X有序半格，有限下令半格
% }, c( X% h4 \7 [$ x  Q有序集
. S% ~$ K2 F; i! |# w% l$ R9 R矿石域" P. e& S- f. N8 Q) W) W; P* D
Ortholattices4 o% E$ `4 \8 F! b6 H, }; d' N
正交模格# C* e4 q% C4 @# K6 k, Q- t
p -群
+ F+ B8 K6 `; [  ~" {0 S$ _部分groupoids
% ]! M: [/ X! E+ P; D9 S8 u& `部分半群
: d1 c) e8 U8 F& c9 A6 L部分有序的群体* S7 f5 j& E3 g: g" ]+ X* Z
部分下令半群  k6 W& @( T* z  p5 V
部分序半群
) o' {7 M9 i" ~4 ^: P  e( S部分有序集
7 c4 _. i4 h2 W0 m9 B皮尔斯代数2 z; o8 h6 o/ R  J
Pocrims( i* U) Y- n' v
指出residuated格
+ ?: C2 d" G' C! _; Y, F' kPolrims
& a/ O& U) ^6 y: TPolyadic代数$ I. }- d" T3 u$ k. E0 F/ @" y
偏序集0 M6 \! }8 t% h+ o8 W
邮政代数
! ?0 Z8 J& m: ^* T, [8 MPreordered套5 ^* v1 J- T4 L3 y  _6 S
普里斯特利空间5 o) V1 j. B3 h/ I  b
主理想域
: k6 ]  M( G2 l1 b! k进程代数
  {6 r; C7 i2 Y" K3 x2 |- g伪基本逻辑代数
. ]9 N" x2 ?9 ~5 w伪MTL -代数' @, p% f1 c1 F2 L
伪MV -代数5 V9 y, f4 ~1 Z* D: Y. ?; \
Pseudocomplemented分配格; J8 [1 G' u- n  O& `% F* `
纯鉴别代数
& @- ?/ K. r) o! p/ \& w, ZQuantales+ a2 X( d1 w7 R& s% S% Z7 |6 f
Quasigroups
' M0 Y8 }8 S& c5 W/ g准蕴涵代数
  j+ {7 s$ f# g# N+ e: Z准MV -代数
% s: b1 z' J& S% @! ^# `; D准有序集5 z+ p, D) W9 K3 K* L. }
Quasitrivial groupoids# q. ^) R+ D  W4 i
矩形条带9 ?) H3 L. A: c% b: o8 P
自反关系
' f0 B8 v, b$ A* i- i, m正则环
; U. F9 u% r/ v, H正则半群
* o; m3 D  K. n8 A/ g" c5 m关系代数+ u8 n$ H7 S' j- T5 c+ [: L/ \
相对Stone代数3 O) L) t- _, X$ d- d# ^
相对化的关系代数, a9 f6 t$ ]; O9 P; w
表示的圆柱代数: w- V6 w) b4 d' b$ V
表示的格序群体
3 E, j8 v; p7 W1 N: T+ E表示的关系代数
$ ?. W2 q1 i: H1 T2 B表示的residuated格
' q, l2 d( I, k" LResiduated幂等半环" {  b; Y! v2 F7 h5 i, y1 W
剩余格序半群
- l4 N+ R# e( |- i9 `, }1 v$ M剩余格
) g4 X. g4 S7 |# D- C4 n1 ZResiduated部分有序的半群0 j5 {4 ^3 N7 u, W: h
Residuated部分序半群' g& F& j: w; d
戒指$ H7 b% K# J: I( u  y2 w* Z4 u2 E
戒指与身份
; ^0 Z; W. {- F$ A: H施罗德类别/ V4 A: U- P) p
Semiassociative关系代数
* j# M/ g, j% t2 c8 b8 e& ASemidistributive晶格
0 c4 |, u* c% [半群，有限半群
7 G- {. V# {/ m+ v4 [半群与身份
+ s. n! V1 P! ^半群与零，有限半群与零3 d" q1 k/ N7 O) f* w' _2 I  V
半格，有限半格  a3 b/ z7 r/ |- l; [
与身份，与身份的有限半格半格
0 U+ m' u; Z% v( o2 L" f半格与零
# I. ]) z; C7 b  L半环7 U2 u- `. G2 v3 V/ L& D0 N
半环与身份
' g9 t, s. N3 q半环与身份和零
8 f1 V# g6 p( M& a) L3 H4 b半环与零
- v7 ]4 a* W2 D9 U8 g+ u连续代数9 {6 ?! d+ L8 g' I$ N: o
集- G7 i: W. [; H) }3 ^
壳
% I; v! N- n7 h6 N2 h) G' e歪斜领域* u9 Y6 G/ }8 V  m0 \
Skew_lattices
# n! a/ e8 y6 V6 R. `* l# K/ G5 h小类
6 G6 c% r3 i2 G. U清醒T0 -空间$ V! x/ @2 K& i* d
可解群
6 k( n" F; K0 B. z  bSQRT准MV -代数- o# L9 P: D; t5 }- `: }
稳定紧凑的空间. |8 d" A: e2 m6 Q) W9 \
施泰纳quasigroups
% a6 W9 @) g# \5 z0 tStone代数# N) [9 ?6 g6 \9 Z! k2 }
对称关系  q" J) z# \( ?" o
T0 -空间
2 t9 Y$ j* ?1 l% P% rT1 -空间# d. F  R7 m; Y( _! p# N3 R
T2 -空间# F; T- `- L5 m: g  r
塔斯基代数
0 Z: |( n+ s) T1 _; y) ]- b- K紧张代数* f0 Q& [0 G( H0 I4 D" ?7 a7 W' M
时空代数2 \' `4 @. W" Z! [  R% E
拓扑群) ]+ F. R  C, S( I& v5 b+ F
拓扑空间8 `# ^5 S/ z- [( I- j8 ^
拓扑向量空间
  Z! d! ?. _; b! Z# s扭转组3 D  m5 f1 m7 ?" ?4 m
全序的阿贝尔群( D; w1 u- H" T+ t' S, Z7 A- Z0 U) b
全序的群体
* @8 ?8 Y3 q9 k. F5 z% |- N完全下令半群
7 L& ?5 Z2 s( i! U7 @" aTransitive的关系, W2 m9 g/ N- b
树
8 r& g( K% X/ ^锦标赛! S8 e$ m  r; Q+ u
一元代数
2 ?3 D  s8 i5 L4 ^唯一分解域: U( G8 V2 p# I9 O- @/ Y6 I7 @
Unital环+ k1 S; G9 f! {
向量空间
/ J, b" ~* P& j( c( d) IWajsberg代数' M0 Z* {: r+ d$ k
Wajsberg箍
) H1 [, o; U. m* z  z弱关联格
! R1 }0 p& t- [" v2 l, }弱关联关系代数
1 }! V1 k7 [' V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



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