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升级   52% TA的每日心情 | 开心 2012-1-13 11:05 |
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签到天数: 15 天 [LV.4]偶尔看看III
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; H% p) x5 h6 k
; j' g. N5 T( q2 Q/ v# H) [Abelian groups Abelian group
8 _+ }! {2 S) C' F3 [0 y: iAbelian lattice-ordered groups, b8 V5 V# U7 z$ ` K, H
Abelian ordered groups! N, U6 g. D B% Y* Z; v0 e* w$ ?
Abelian p-groups% L) j' X" \3 b8 y) E/ X) y3 @1 p
Abelian partially ordered groups
3 \+ A& N7 y9 LAction algebras Action algebra" P- ~' g2 z; ^2 V/ m" `* O% G
Action lattices; `) v! R6 q" u; {" e9 ~: r
Algebraic lattices
) N8 Y$ ~( W. u" D$ \0 WAlgebraic posets Algebraic poset
) }8 S+ B! S- }5 b2 [Algebraic semilattices! U8 X& `8 Q" \
Allegories Allegory (category theory)
- W5 l: Y) Q* j; S/ z; LAlmost distributive lattices% \6 f0 H( e, ]2 J0 E+ f, l
Associative algebras Associative algebra+ F" B1 w" E. n$ U
Banach spaces Banach space+ G3 V. H5 A/ X8 z
Bands Band (mathematics), Finite bands' D1 Y6 y* }. i* z0 A2 C( j
Basic logic algebras/ ]& g# v) @6 S- F- C
BCI-algebras BCI algebra
% [3 J/ q7 s! v* r& @9 @BCK-algebras BCK algebra
: O/ M. s! E8 Q+ T2 ]( W' hBCK-join-semilattices
$ y# v4 E+ w' Z3 F' O3 D) m( w9 T! U$ sBCK-lattices: {2 f& x4 z" f$ H& F/ u
BCK-meet-semilattices
6 h$ P) s( [* Q d: B5 CBilinear algebras
. n7 @5 g5 e& e4 z* h6 Q$ kBL-algebras7 h1 g/ ]; T3 n ^4 ^4 L+ {; r- h0 \
Binars, Finite binars, with identity, with zero, with identity and zero,
2 U% A Q3 v( Z. j% b$ dBoolean algebras Boolean algebra (structure)
. a/ S; ^; c, p+ \Boolean algebras with operators
2 E0 @+ x) {2 E+ IBoolean groups
" z2 v; h8 l! z) |9 Q' DBoolean lattices( ?0 A+ I( q m P
Boolean modules over a relation algebra+ l4 m/ I& `! H
Boolean monoids
3 U2 S2 \( A: F4 O" `% |Boolean rings
. n% Y) ~8 |$ o( I) x; Z' uBoolean semigroups
1 C5 E: x# E, a+ f, \' b3 uBoolean semilattices/ z% \9 m V/ n) I
Boolean spaces
% {$ s7 o. r* R# q' B8 ?. b$ ABounded distributive lattices( ~4 J: o$ n; o/ R/ e- r
Bounded lattices
l" J: U0 E6 l. }, }- pBounded residuated lattices
, x8 M9 x' X' ?/ sBrouwerian algebras; \4 n" h! T& }( \! k$ Z
Brouwerian semilattices
6 V# q7 |3 o4 R, GC*-algebras
8 V9 ^% p% a% G" CCancellative commutative monoids
, T& ^9 ]& A! i3 H# A$ [Cancellative commutative semigroups; I( L0 T$ ~6 A% }8 m5 N; h" Q
Cancellative monoids5 s& g! B/ A8 g3 V7 o
Cancellative semigroups7 d% {0 ~( R" [7 p2 b
Cancellative residuated lattices
1 \, `& i1 V3 FCategories7 |8 M* W: H8 i' F+ Y5 r
Chains
- K$ C2 k- F \7 m- P( U. zClifford semigroups4 g* q1 S+ x) t! N( N- n' i, a. T
Clifford algebras
, U0 K% k/ G3 E% m7 }: PClosure algebras
9 j6 c7 [! G, {2 Q9 O8 o0 H/ c4 eCommutative BCK-algebras
9 Y( |. t% g0 `: ?5 a' Z) U# |8 W* `Commutative binars, Finite commutative binars, with identity, with zero, with identity and zero 0 w" X4 `' q# T( N/ n' p s3 N
commutative integral ordered monoids, finite commutative integral ordered monoids$ j7 t; m$ J3 O8 s$ J7 r6 z- Q
Commutative inverse semigroups
+ B/ w" g; e# ]. ]Commutative lattice-ordered monoids
: L W$ }& o y8 \ L2 c jCommutative lattice-ordered rings
' w( W% T; u# [1 x6 c& _+ HCommutative lattice-ordered semigroups; j4 [, E! Z2 C
Commutative monoids, Finite commutative monoids, Finite commutative monoids with zero
$ w4 i6 e! ^+ R1 b$ G1 Z. h zCommutative ordered monoids ~2 o/ G: W0 f( X
Commutative ordered rings
' B6 v" V8 v* S0 z. R" I1 c- dCommutative ordered semigroups, Finite commutative ordered semigroups4 J! |8 ^' j$ V6 [5 K
Commutative partially ordered monoids
- e$ W1 U+ w. pCommutative partially ordered semigroups( ~( b. x) v; `+ C7 Y6 x1 G, ?* n
Commutative regular rings* f0 W6 O4 G) C2 L0 n' f
Commutative residuated lattice-ordered semigroups& v# u2 G h0 |$ ^5 q! v. t3 p9 c
Commutative residuated lattices6 S9 P8 h5 ?/ Z/ [* K4 U, D9 N
Commutative residuated partially ordered monoids# X5 C- J$ \& b9 q5 N
Commutative residuated partially ordered semigroups
5 {# f( U' B! K8 x1 _& LCommutative rings w# a+ w: s1 S, ]/ R
Commutative rings with identity7 E& ]: f. k, l: J( {
Commutative semigroups, Finite commutative semigroups, with zero5 Z d, J- Y& D+ ?2 A) z& w
Compact topological spaces& Y5 j* o! L% |. S
Compact zero-dimensional Hausdorff spaces
3 F5 `- x. r! Y, {/ P/ WComplemented lattices
! t( G, I2 g$ OComplemented distributive lattices" Q; D2 U+ Z" v- b
Complemented modular lattices' _" j$ K# g2 ~2 y- D
Complete distributive lattices; u1 I j& O, A$ F
Complete lattices* y* k$ ?% q6 X% e. ~' O' ?
Complete semilattices
; s( U6 E! X; f) Y, i! p6 g& sComplete partial orders/ p0 M7 g# `9 _4 l: q: c" p* B
Completely regular Hausdorff spaces
) R) J3 X9 _& Z9 ?! p6 A5 M( S- FCompletely regular semigroups
|& |0 h0 b9 R8 EContinuous lattices/ u. ~" H# L0 S: f' ~
Continuous posets4 K: Z9 ^. w0 k; E! g, K" ]% w
Cylindric algebras
# F4 f O6 t6 j" X1 R8 T6 KDe Morgan algebras- t0 P% J; h' @1 R* n
De Morgan monoids
4 a# R2 Q/ S# @& a* q0 X3 U: jDedekind categories
, F; P2 a$ b' y. Z* `5 HDedekind domains
, j1 f L+ i$ Q5 D2 [Dense linear orders( V; K" [+ `8 q7 j+ p' x T
Digraph algebras
& O' Y; p' L6 K% p2 \Directed complete partial orders
1 g& y! Q9 Q9 Q( e& {5 X. ^5 PDirected partial orders9 d, N9 w+ c' R2 y$ t
Directed graphs
, P1 F0 C/ T( \2 h: o: iDirectoids
2 u. q( U+ S9 UDistributive allegories
7 o- U0 S8 Y$ BDistributive double p-algebras, K5 Z2 N. T# R: d% J
Distributive dual p-algebras
: }+ Q6 S! R7 LDistributive lattice expansions
; Z5 G2 C! Z% n1 q) B8 {$ nDistributive lattices
5 Z$ L7 R* E1 Z, _) J c4 w dDistributive lattices with operators$ R% l$ @5 W- }5 d& u. s ?
Distributive lattice ordered semigroups
9 H Z0 Q4 W9 A: }Distributive p-algebras+ e: L# {+ [+ ~4 }; c% v9 N7 I
Distributive residuated lattices
% J1 J' R: C0 @ K+ kDivision algebras
4 Z/ V# B$ R% g v% w7 T! w$ uDivision rings
! L3 i6 R* j( O! N3 W! E( [Double Stone algebras& H% {# l) I$ d4 R1 Y$ M8 n
Dunn monoids
* b/ A" Q2 E- G' IDynamic algebras& c7 [/ K; H$ K5 l" \2 I4 J+ Y
Entropic groupoids- h; N+ @$ H. G3 x5 F4 `
Equivalence algebras
" C9 _2 C; b4 `2 wEquivalence relations
9 {5 h: v i6 C" G" Q( }! CEuclidean domains
1 l4 F' e$ s/ q( l9 |. v3 O$ ?f-rings% A! T8 k$ Y O* A8 |
Fields
3 ` I0 B' K7 g9 [! }" g! yFL-algebras2 f/ X7 w( }/ i" h
FLc-algebras: P6 h9 O- C1 o9 X: G4 U2 Y. m
FLe-algebras
2 y0 m- L" j4 I6 L+ ?FLew-algebras" {; V+ i" B5 r9 x: H8 v8 b
FLw-algebras
2 B1 E/ C9 h0 R9 ^8 k* b! iFrames$ v/ V$ q2 {$ C1 c4 m' \
Function rings
: c. X8 A! v# i" h) N! h+ FG-sets
- ~# M. \/ d5 ^; L( uGeneralized BL-algebras9 M5 |! d/ x0 N0 [, B
Generalized Boolean algebras4 O% e7 L, T! R9 _5 b, v4 L
Generalized MV-algebras
; v5 n/ Z0 l% c) f" ]; _Goedel algebras) Q. ^! u6 C: v9 _3 F
Graphs; X- R) }5 P& X, B
Groupoids
: @4 j, F" p6 UGroups
, p P2 y; i0 EHausdorff spaces
0 f- F3 \5 H! e: M% s/ n5 ^* IHeyting algebras
' Z. X9 S; V, v+ i9 L; G- \Hilbert algebras
' Q$ p9 b' x1 E2 R9 s$ L! W- Q9 cHilbert spaces
* C# Q0 n, z% p( M0 D2 v4 _8 l% \Hoops
- Q6 N% k: _* f- y4 [( YIdempotent semirings
9 j) c3 c8 z$ k, N7 D% MIdempotent semirings with identity$ t% B8 o, |% K' ~* W
Idempotent semirings with identity and zero
?& k1 V7 w- V" s; qIdempotent semirings with zero
1 T& ~* K5 j% E' ~+ X( dImplication algebras% d6 I2 y# u" }
Implicative lattices7 n0 P9 C" W8 C/ U
Integral domains
! a' h- L6 ^6 tIntegral ordered monoids, finite integral ordered monoids9 W7 {6 |2 W8 d: Q
Integral relation algebras; i' ^' B( E! M& W& p
Integral residuated lattices
' u- O, Y1 y1 i5 T$ \/ R( |7 J. eIntuitionistic linear logic algebras
' G, h; Q1 x" \+ f# ]7 C7 YInverse semigroups- O( i B, X) p7 |
Involutive lattices' w7 I; U4 k- o! @2 \# w
Involutive residuated lattices
( n$ [' d( w/ `Join-semidistributive lattices2 _) [) r/ S0 b; e0 A& h" _
Join-semilattices
, z( g! e; p$ E7 |! KJordan algebras
* I' [0 T" f, C4 sKleene algebras
1 b8 p' b3 T/ ]- a: x5 MKleene lattices% n$ d6 f1 M' I. ^$ W* r3 d; Z
Lambek algebras) j+ Q2 e) g# W2 n( k
Lattice-ordered groups7 t; Z* |5 R& O
Lattice-ordered monoids
8 P1 _; `3 G5 E) H8 |- \* K4 nLattice-ordered rings
& A6 T8 P: R. ?+ K8 p6 ^% k$ lLattice-ordered semigroups6 ]: i; C" p9 y/ j9 u
Lattices
2 _' l' r7 D: [* L+ b; ~& x8 k9 @) M4 bLeft cancellative semigroups
y7 ~" ~9 Y' z, j w) fLie algebras N3 {% U: n# u4 c
Linear Heyting algebras
) I# q+ I, x8 B+ a4 `Linear logic algebras
' ^+ Z+ `/ H0 s' W4 i! @- ELinear orders: H# r" B$ P) ~+ m5 p
Locales2 a3 F2 P U8 h1 Y2 r
Locally compact topological spaces
' Q1 z3 S- w' e; o( p7 JLoops1 c1 Y8 v$ r/ c6 l6 h; Y
Lukasiewicz algebras of order n- x: L! Z0 s' _, U
M-sets9 ^* G& n8 j" {1 e; Q: e
Medial groupoids) L7 N* z0 m- e' |8 L( x
Medial quasigroups5 k" e% i3 G0 Q( n- |. k+ m% h; d
Meet-semidistributive lattices
( ]8 M8 s5 s. a/ d y; I$ kMeet-semilattices. Y; S5 j! `# l
Metric spaces
! j" b; v' m5 b6 @2 \5 m" N j a; QModal algebras) o& K' T# q, b& d- `( I
Modular lattices
$ ~ {! _: i6 G# q8 ~Modular ortholattices+ e: B! S& z( N; k* P7 a# i
Modules over a ring
$ L% m3 j! O2 E/ l9 Z) u$ F; yMonadic algebras8 ]$ s$ I3 q) b$ w8 i/ x0 U
Monoidal t-norm logic algebras, U: o( I$ H, }8 t
Monoids, Finite monoids, with zero4 r8 k H4 v3 f( B
Moufang loops V; t0 K! |5 z4 e
Moufang quasigroups% _- @- c7 \' L; @# l! a* O ?
Multiplicative additive linear logic algebras* o3 [- ~; z; ~8 s3 r1 H7 j/ I7 @% x5 {
Multiplicative lattices( T" U6 U' B% e
Multiplicative semilattices
/ z3 }( j. E$ j: lMultisets
1 ~: ^! Q( k) W7 D3 f3 i' c2 JMV-algebras9 q. y3 b7 }: F" P
Neardistributive lattices, l- x* j; H0 K2 b: @0 F0 w
Near-rings
% n7 A& H7 E+ F6 O: l8 x6 T% Y5 ?Near-rings with identity
# I& l% N) R, S6 wNear-fields
5 `% g+ q+ w4 u! s8 wNilpotent groups3 O: i- O: {' l: R( A0 B
Nonassociative relation algebras
5 M# x8 A5 M$ w$ nNonassociative algebras
; c, h* \0 [/ R+ x9 eNormal bands
( V& M# B' T# P2 v! D" \- d' SNormal valued lattice-ordered groups5 I5 l7 ^% }) H M: P* R) f$ }
Normed vector spaces
" D9 P# D5 @4 K% vOckham algebras& _* `* O6 }+ G) d4 B; ~
Order algebras, P" X. Z5 v' c8 q5 J3 v. V' t
Ordered abelian groups) t& z* O1 ?' t
Ordered fields, u7 p8 G# d& L, Z l3 v
Ordered groups3 M; Z( o/ |! R1 u( W( m
Ordered monoids; @+ e1 Q7 Z! O+ E
Ordered monoids with zero" \* J# Y3 n4 v( Q- i$ p9 l7 R- F+ O
Ordered rings
5 k2 E ?" b- @0 P$ d. ?. S6 `Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero4 z6 n) M, T) @) Q) Q
Ordered semilattices, Finite ordered semilattices
/ V$ r# H- z9 G/ yOrdered sets, W; V8 p* d2 ?2 \
Ore domains
9 l4 o& N$ L5 M3 Z5 HOrtholattices
9 L7 q0 I S7 d, @Orthomodular lattices2 H0 K6 ?) M& y1 |5 R
p-groups
0 ?4 K, ]2 W& d1 W. ?& {Partial groupoids1 I: S8 R; N6 T2 T
Partial semigroups1 Y/ F" j- {# y! S* ?% w& Y. m' g1 t
Partially ordered groups- |4 p- f. f( n3 f. H
Partially ordered monoids1 V# [% [9 o+ Z# `, \
Partially ordered semigroups! \; y: C( ~3 g! |1 C9 _/ h7 W
Partially ordered sets( T* ?" t; |7 b3 R' a
Peirce algebras: s4 V3 G4 s/ K7 f1 ~/ N
Pocrims
3 h$ o9 { j4 R+ W1 s" gPointed residuated lattices& S! S$ v$ ]7 o: x
Polrims
% k/ G. ]1 l# E2 |( d; C$ tPolyadic algebras
6 H: a2 m v: S* ] d* u) a0 \: rPosets
. b" E& e/ z3 W8 m, m$ \6 A; EPost algebras
9 N& w/ ^- h {6 V) l3 DPreordered sets" \9 h" L9 W; i m, [5 p
Priestley spaces3 [+ d+ s6 F) ]- E( k, [2 E
Principal Ideal Domains
/ E1 Y5 d, `) n4 A6 yProcess algebras/ r! _' C* _% e' g7 e$ d, k7 Y
Pseudo basic logic algebras3 o; J9 @' {; a% J" K, |* E
Pseudo MTL-algebras
* @- \$ E. Q. `9 s- k# i5 uPseudo MV-algebras5 J) n$ z6 P. Z! F. L8 n
Pseudocomplemented distributive lattices
+ Z1 ^1 M" p( `1 i9 M. `# RPure discriminator algebras8 j) t# H: a4 o: {; }3 P# {) v( z
Quantales) b$ h+ e' ~- R' W, r+ R
Quasigroups
1 [, ^% }# _ t4 f9 V0 D. o5 z8 }7 VQuasi-implication algebras0 E( E% e3 Z9 s/ R
Quasi-MV-algebra- h& @0 A0 u9 ^& X0 U. w, d
Quasi-ordered sets9 q- z- ~. b* F6 g- {, g
Quasitrivial groupoids
; {8 m3 @; B) Y/ q L( q( PRectangular bands& _6 D% J4 X$ a% y$ Q
Reflexive relations
1 E) J- x. @: z! RRegular rings
! C: ?1 j$ u+ tRegular semigroups
9 ^7 M, s' X8 w. V$ X8 dRelation algebras
' Q2 ^& W& F# {8 D2 [- T, TRelative Stone algebras9 O- U5 O1 C y
Relativized relation algebras
/ Q2 V- L* Y8 i6 j9 @Representable cylindric algebras
/ _# a! g9 o- `( `4 kRepresentable lattice-ordered groups4 K# g* B& U7 w/ U# K
Representable relation algebras5 a% b5 l; ^6 d: l6 r$ B
Representable residuated lattices
' {1 D. B% S w1 H% SResiduated idempotent semirings* l% w* f" s9 U7 D s5 K
Residuated lattice-ordered semigroups- h( k0 j3 {( |" i. L
Residuated lattices: c& s `" D6 @1 L. M( E
Residuated partially ordered monoids
7 o1 j$ h3 k( p6 `0 J1 m9 A9 |Residuated partially ordered semigroups
0 G' U3 A% }" o! c: |Rings5 f' }1 A* F' d- X/ G0 ^$ A* ]
Rings with identity9 J1 x! q+ p) A% T2 O# w9 c
Schroeder categories
+ s }: b- c& LSemiassociative relation algebras! D* Y8 U4 M5 \! m8 K7 W# E
Semidistributive lattices9 O- n- c( r% O) T
Semigroups, Finite semigroups4 u* e: }- j f' c, b
Semigroups with identity, O r2 v, i# e M# i) x
Semigroups with zero, Finite semigroups with zero8 L" W9 G- |$ c W! t
Semilattices, Finite semilattices- ^$ n1 M# c" b/ S% G8 a& d
Semilattices with identity, Finite semilattices with identity8 @4 V/ D& g2 d$ O# A
Semilattices with zero7 ~& D8 Z3 Y' w: g, V4 }
Semirings" q i+ S- \& m
Semirings with identity
! G$ j+ x* f( OSemirings with identity and zero# r; @. `8 P( \/ X0 o
Semirings with zero
! i2 k& P( [# Z2 }Sequential algebras$ |5 n3 E8 y: O. z8 H! c' N
Sets+ |9 z0 F7 Q3 G7 ]9 W6 I
Shells
5 _& U+ e, k* U2 X' v* ZSkew-fields
1 p) E/ q6 w8 H. l. l; ySkew_lattices
$ k. S3 s2 f- h. E8 nSmall categories% O: E6 p- Y M4 E! ^
Sober T0-spaces
& Q$ ?: t" n; p% qSolvable groups' G$ h7 H3 J( X' j3 J1 @- i
Sqrt-quasi-MV-algebras- k5 a* g5 `6 A
Stably compact spaces+ }* A/ s3 a0 n$ ?- V
Steiner quasigroups
# I6 U# T8 B' J1 Z- w8 u1 \Stone algebras! a- m$ z& t- Y0 r
Symmetric relations8 h, j- i+ T. x: z9 N
T0-spaces
; \& m9 f2 @& j4 \! j" cT1-spaces# W% p( k, ?7 g9 S; G, [. s( R9 W
T2-spaces
6 ?2 z9 Z- \6 i4 r- sTarski algebras
( @( d G% y# jTense algebras
; l- _3 @( _ t# KTemporal algebras
) f E R- \: L2 e. h+ RTopological groups8 \) v( Y# e# n4 M1 I0 ]9 `& D
Topological spaces
7 z5 a+ |' N3 f7 J# iTopological vector spaces
! v; t( R c1 r% tTorsion groups) K g$ f. q6 |% i
Totally ordered abelian groups
5 ^8 F' q# L, }9 G. J; {5 lTotally ordered groups1 n3 V1 P* e0 n |/ q! S
Totally ordered monoids+ ` t' E3 F( Z+ C/ k: A
Transitive relations
9 N$ t/ \2 Y4 a4 {2 s3 WTrees; E4 V& c9 |# ^
Tournaments0 p, H5 g! I. q$ B1 v+ P/ p
Unary algebras. M) k; |) R0 ]" R% F. o/ Z+ @
Unique factorization domains5 V J; F$ K+ i2 |% O$ R
Unital rings7 ~3 F4 S9 p {
Vector spaces9 |9 ~( D1 e! k0 P
Wajsberg algebras3 [+ w$ L1 e5 [
Wajsberg hoops/ F0 _; G& Q9 k' C: _7 x6 X
Weakly associative lattices
) F5 a7 C- ^+ I5 ?5 ]8 x9 JWeakly associative relation algebras/ g, \. y; l! J5 r9 e% {, h5 W2 i
Weakly representable relation algebras
4 L3 E/ F! k) K, q; W, B! E; l2 S# A |
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