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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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0 |* v+ F. Q M* x7 j
Abelian groups Abelian group0 Q. `0 W4 D2 X1 G" G% V: s
Abelian lattice-ordered groups
/ A- d+ b" [0 U! m; ~4 W! {Abelian ordered groups
- M* S/ b% M& p% O) xAbelian p-groups
/ G2 E" D' I. ~9 ?. `. iAbelian partially ordered groups* A+ V+ Q2 Q9 X _
Action algebras Action algebra
, T# e+ R: c; X+ Z& a$ b* YAction lattices0 r; b" ~: \% K/ b2 V( k
Algebraic lattices
. ?4 g: B" {/ f, T: C2 hAlgebraic posets Algebraic poset: `, d u6 s- j, t
Algebraic semilattices6 y6 o+ `! a9 G) ~$ z
Allegories Allegory (category theory)
4 w' e/ m$ |5 H1 W- L3 RAlmost distributive lattices2 V; t% [0 Q% J+ h+ e) e, |
Associative algebras Associative algebra
! ~0 w) q4 x; y1 {' l, J1 fBanach spaces Banach space, `6 k) ]7 _, X V" o
Bands Band (mathematics), Finite bands
0 r% C/ v2 ]9 a: {1 }& f) KBasic logic algebras2 N7 s, ?2 e3 X7 @
BCI-algebras BCI algebra/ K9 i9 i( v$ S G% P4 w6 }. ^! l
BCK-algebras BCK algebra* L9 m' c8 o& Q- c
BCK-join-semilattices/ d, G0 b% \* j" Y+ N" U
BCK-lattices& ~, u k' Y0 x( ~
BCK-meet-semilattices
4 ]1 U- L5 R9 A0 X! HBilinear algebras |8 ?% v9 G) L5 B T4 v3 L
BL-algebras
e( @. g. V" G3 [- f. O8 h- EBinars, Finite binars, with identity, with zero, with identity and zero, ( @5 @, r0 o1 a# ^
Boolean algebras Boolean algebra (structure)
m% [) ^% t V! }. X" gBoolean algebras with operators
, `7 W& x6 V( a8 x7 T bBoolean groups
7 Y2 L0 H: F9 U) ZBoolean lattices
5 G$ x- v/ {" z( @5 I# o1 ABoolean modules over a relation algebra
, H1 u- O: ?- R# F8 J# v0 WBoolean monoids
5 i! N$ I& i4 m% m1 a% p' hBoolean rings
! f) o& O% p0 L/ l/ W$ {Boolean semigroups
+ i" _/ f, k( g" Q1 dBoolean semilattices1 U& B/ G" X5 j% @5 x+ Y0 B( u t
Boolean spaces0 f1 C# z3 {! O/ L: U( I) Q6 ~
Bounded distributive lattices. V5 ~, z, ?- D
Bounded lattices' T0 \8 x1 j( y2 `2 r1 U
Bounded residuated lattices$ B+ y+ o9 c2 h0 s6 t" _# _
Brouwerian algebras
, h& U+ @, T( QBrouwerian semilattices |9 |3 ^+ Z8 w. H) J. v
C*-algebras
4 i* w' X1 Z; ]6 g8 c: n2 ACancellative commutative monoids) B! s& @: g( q; R
Cancellative commutative semigroups
9 M; y# @# q# s' bCancellative monoids
4 J8 c# ?" m- t" u, ~Cancellative semigroups$ h/ s+ `( z7 h% w% k
Cancellative residuated lattices
+ X9 U3 _: L6 jCategories
" H4 O z" ^- UChains
. `$ W( _6 @; O: |6 Z+ b, SClifford semigroups
9 W2 l8 T& |/ a! G* RClifford algebras
( n5 \! }' S5 l% kClosure algebras$ u1 d" N; O! o+ d
Commutative BCK-algebras
3 ~# L0 B3 C) K) y6 M$ A3 f, A4 ICommutative binars, Finite commutative binars, with identity, with zero, with identity and zero
4 ^) d' [) }: h, b) m" A- |7 Fcommutative integral ordered monoids, finite commutative integral ordered monoids7 n. k* m2 B, E3 f
Commutative inverse semigroups, N T+ T, f! P, h
Commutative lattice-ordered monoids
2 |2 Z5 _1 I* W3 nCommutative lattice-ordered rings& i! V2 V: u2 E* Y5 Q3 z
Commutative lattice-ordered semigroups
. |' h" p Q" H$ ~) i( qCommutative monoids, Finite commutative monoids, Finite commutative monoids with zero
& m! H: }5 n5 [0 uCommutative ordered monoids* w8 u' ^) u7 n1 U" r
Commutative ordered rings
- g% t. _' r9 e# [/ c- ~# \) GCommutative ordered semigroups, Finite commutative ordered semigroups+ P6 O$ @4 m, z2 K
Commutative partially ordered monoids6 W4 b3 l5 ] q2 g2 j
Commutative partially ordered semigroups
$ H5 q8 d( r4 f; CCommutative regular rings- D3 x" E U2 y. l) h
Commutative residuated lattice-ordered semigroups9 S( p# b2 K3 z
Commutative residuated lattices
! I- U* N+ l9 WCommutative residuated partially ordered monoids5 p' {% x2 P7 F# P d: k& B
Commutative residuated partially ordered semigroups
1 B6 E; ?& r) v+ }- }+ H% f& OCommutative rings2 q& A7 M1 {9 U& K: M
Commutative rings with identity
5 b( ]1 ~( i6 T0 ?Commutative semigroups, Finite commutative semigroups, with zero/ i5 W% M# M4 _! `) W/ X) E* u: _
Compact topological spaces9 O. b, }* H4 H9 x2 E4 `
Compact zero-dimensional Hausdorff spaces
* t9 X& H) R- d2 f# v. h' ^Complemented lattices% d2 j5 ]. s' C
Complemented distributive lattices
6 [/ y7 r1 Y% n2 v" EComplemented modular lattices; ?; f$ n0 v! u1 J( O* S0 d
Complete distributive lattices5 U& c2 P, \& w; S4 [3 R/ T, ?
Complete lattices. {& T4 Q! @7 c( _7 o
Complete semilattices+ i) _, I) u; I& J3 a
Complete partial orders
0 M. N4 z1 V6 _0 E! O* yCompletely regular Hausdorff spaces
% j# R; f! j2 V4 I# E. ?# `* }0 hCompletely regular semigroups" T/ A6 E# L5 R% f5 c0 v6 |
Continuous lattices" ^ K2 c2 F4 _3 u, \
Continuous posets# `4 X6 ~& i8 Z3 D6 N! o( R# S$ U
Cylindric algebras
! h1 l$ @0 j) V3 F9 gDe Morgan algebras8 }* y9 {3 s! l R) F! S7 e" {
De Morgan monoids
6 |9 Y5 t9 q! c! p& q. VDedekind categories2 p9 k3 v: J. W: u
Dedekind domains
* ~$ i1 c# p" l- o) ^Dense linear orders
, t! D W6 C0 D3 qDigraph algebras
8 @/ m7 M+ y: LDirected complete partial orders
; N. g( C& g2 O5 q( r& T ]* QDirected partial orders
$ Z+ e- l/ C3 G' l' [Directed graphs, ^, c* i2 E# g$ A+ |, ]
Directoids
, k9 e0 @) j0 D3 C7 q/ e) vDistributive allegories
" K9 f9 z! X# V+ F' yDistributive double p-algebras# N6 ?' b5 P2 d1 ?
Distributive dual p-algebras! L0 ~3 x6 D; ~$ T! ^9 h
Distributive lattice expansions
( d" U1 Z# @3 X! `) e. I: DDistributive lattices$ W% K2 f. _& Q* d- f' h9 p
Distributive lattices with operators
; n {: [: B/ E# uDistributive lattice ordered semigroups0 S2 k n! e! C4 w2 \
Distributive p-algebras: H8 E3 ^; m% R8 z
Distributive residuated lattices6 g [' d0 K M1 A( N2 s
Division algebras
: a$ P/ J# i0 K, B' [Division rings& z# }0 p2 [" }
Double Stone algebras( N7 D- ^8 j5 ?3 I& b" r2 N
Dunn monoids
- m+ L. P, K7 B8 q$ t- _2 wDynamic algebras( a k7 U$ n% A6 ~4 ], @' s! ?* k
Entropic groupoids( c% n% c4 l1 p( a8 y. J: S
Equivalence algebras8 I! o) z* L2 Z/ C0 A
Equivalence relations& k" _8 h0 l3 z' R' y
Euclidean domains5 Q! h5 ?0 i& @% {4 F. m4 v
f-rings$ V i5 v2 ~/ n4 r$ _* J
Fields
) E+ l3 ~6 S7 l4 s% w! t' s" N) iFL-algebras
, E- O. g9 l' p% e8 BFLc-algebras4 u5 ]: a4 M# E# w" M, V
FLe-algebras! r' y( \( y3 w! x' S8 [
FLew-algebras# J( B1 X) r! ^2 `8 k% k
FLw-algebras
7 z7 `" x( H! `/ fFrames! Z2 x5 B$ @& q) o
Function rings7 a0 M, l( Y+ W4 C- e; Q
G-sets
* P! |# Y% Y0 B Z( u! F* I' hGeneralized BL-algebras
- o3 y0 b k. T1 ^Generalized Boolean algebras4 }7 W/ C8 V4 j1 a" [5 w
Generalized MV-algebras
* P' }! z' g1 O y7 |Goedel algebras* q$ H0 j8 h2 {, X+ a" _/ o
Graphs8 w# F- U C* M L! O
Groupoids
& l7 a* J' `' `Groups
3 Q1 `& k1 A# A; k7 m" Q6 aHausdorff spaces
% a7 M u \7 M9 ?! V8 h6 SHeyting algebras
9 e) m i4 l$ S3 h, `4 PHilbert algebras
) v S8 S% ~: t; LHilbert spaces
6 ^( ^) V, [& ]1 Z* P. cHoops7 P4 o$ X7 D9 T
Idempotent semirings" n- M1 U! v0 y
Idempotent semirings with identity7 e. z4 ]8 l4 a5 A( d. L- G* H$ U
Idempotent semirings with identity and zero5 ?1 R6 o* b3 d' P; V I2 _
Idempotent semirings with zero' t8 m. p2 E6 J9 e+ ]$ O6 s! L
Implication algebras
9 W6 U; @6 m& P* ?Implicative lattices2 P0 Q, I4 }2 A/ G. F# e
Integral domains
0 K9 m- P7 p3 i& L) kIntegral ordered monoids, finite integral ordered monoids$ W- R& d9 q4 f6 h
Integral relation algebras7 m4 | j- h5 N
Integral residuated lattices2 F. p9 a. M) \: a
Intuitionistic linear logic algebras4 x" p6 g" _4 \; q# j
Inverse semigroups
. t- a; \/ P5 l8 Z4 ]: mInvolutive lattices
: g( C: B" B4 BInvolutive residuated lattices$ J! R% w2 _+ M, L) u7 y
Join-semidistributive lattices
1 Y" J' A, a/ L9 D, W* q0 lJoin-semilattices
7 M1 K3 O$ R/ i) Y7 D: I. C2 ], ~Jordan algebras- N! \* s0 \/ G6 Y/ O
Kleene algebras0 x+ O9 E* `6 G. U \1 r
Kleene lattices
, ^0 W9 Z: S- E* `1 j' W' ~Lambek algebras
* n0 @* M! x# k$ V, k0 |- dLattice-ordered groups% ^, P5 Y2 Y- _2 W, O' }
Lattice-ordered monoids
- K k6 B# I8 ~2 j5 O* f: c. p* S. PLattice-ordered rings
& C e, @1 b) v& {- cLattice-ordered semigroups* q, ]$ [0 k" e4 \9 C0 X
Lattices8 n' J* O* u" `, B; g
Left cancellative semigroups4 f2 T8 h+ `7 a# v& \1 U
Lie algebras$ e! ~* s4 Y1 i/ ^6 H" X
Linear Heyting algebras" S; b- e3 m" i4 h' j; H5 M
Linear logic algebras
+ _2 J. X( ~ Y) K% ]9 mLinear orders
. j# g* g& |$ I' \5 O1 eLocales; d6 i$ b' }, a
Locally compact topological spaces0 G9 Z9 f8 L% ~9 ~* \4 u. F( b
Loops
0 l. x" d9 A! Q9 |7 c. BLukasiewicz algebras of order n2 ?) B6 u4 h7 z {& a
M-sets
! O* f3 H# ]& \; l7 BMedial groupoids
; \+ Z. r; O+ y7 S. p8 mMedial quasigroups
$ B& d! i% W+ X8 l1 m( | e& mMeet-semidistributive lattices
* z) L, L8 f% @. G! N7 _2 ~8 t, r* vMeet-semilattices3 q! p T( ^# k4 f7 A0 G
Metric spaces
& U& z9 f/ `: V* b% q/ HModal algebras" |1 j5 [5 [# ` Z
Modular lattices* S; S* O& Z/ D n7 I" g
Modular ortholattices
) n( j3 K6 b6 v6 b2 mModules over a ring& r! P! r5 Z" d8 j R8 M# U! ?. y
Monadic algebras
, |+ Q3 _5 u" q2 {& ^Monoidal t-norm logic algebras
1 T' K- q( ^* y4 z, G7 u3 x9 `8 \Monoids, Finite monoids, with zero1 O; G9 G7 _6 ]
Moufang loops. Z7 a" b z$ ?3 R/ G
Moufang quasigroups
: I+ g/ e8 l/ |' A' o5 mMultiplicative additive linear logic algebras, c1 W2 v4 z I6 E7 l* S& `
Multiplicative lattices0 U. j; w5 h) F0 p. C
Multiplicative semilattices
$ }$ J! y# P& h( S- }Multisets" n3 z9 s7 A5 E2 ~
MV-algebras
7 M* D" V- t. ~- J" bNeardistributive lattices+ n# u' n: e" A! h# M
Near-rings
6 ~' W2 W1 ~& @; W4 FNear-rings with identity
3 D& }) Z8 f0 G7 T- F9 W0 hNear-fields
7 l3 [5 e1 J+ f$ Y& K, k: R- o" |Nilpotent groups
$ ? I& \& m* x+ I1 a9 SNonassociative relation algebras
6 P% O1 m! y! ]Nonassociative algebras
' R! `5 h. A: K# {8 L8 z% BNormal bands; o5 v/ Q. l- Z
Normal valued lattice-ordered groups
: A% |8 t+ m! v) NNormed vector spaces2 ~9 k% F0 |" |& T8 {
Ockham algebras
2 {; k0 Y, u; R) v% d) NOrder algebras u/ a& ~: [8 T6 ?
Ordered abelian groups* S" o w' L( k, V! s
Ordered fields! ?4 q8 d! f( z
Ordered groups0 b* S# A: U' W+ W7 w$ O! j
Ordered monoids, S. F8 G+ e- s- N7 F j2 C- ]* ]9 Z
Ordered monoids with zero4 t5 b! D; t: g) T# ?" q9 [2 v
Ordered rings
# j6 |% ^" a2 HOrdered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero
. E( u* A4 m% c* x" a; E# sOrdered semilattices, Finite ordered semilattices( x; P' w2 t7 ]
Ordered sets
. ^. u, `5 I) E& ?& E6 UOre domains3 ^4 @6 i- F$ [ U4 o7 \) K% |* X
Ortholattices* q. I5 N w; G9 K% `
Orthomodular lattices1 y* f6 j1 ]( Q' J9 [ x( _7 x
p-groups' s: I8 z# y/ W& _5 Y
Partial groupoids
* e4 E6 s3 j4 B) ^$ x. \" TPartial semigroups
0 h9 m, L, t% t$ h- a* g7 B9 qPartially ordered groups
4 _5 {0 @. [; f {1 A% P! W0 k+ NPartially ordered monoids
@7 V' }& w8 QPartially ordered semigroups
6 W u m7 Z) d+ ]: `% lPartially ordered sets' j' b9 y: U- o
Peirce algebras: B @6 R( h0 Z1 b; P, r
Pocrims
) J# ?7 B% P' A* cPointed residuated lattices6 _& s( m+ ]5 K" U- p8 T( h/ p
Polrims
" B3 J; X) B- g r6 I% L0 dPolyadic algebras0 Z5 I0 l) j5 ]( i* v
Posets
1 T# w3 a$ F: r) b. bPost algebras9 @. D1 |6 C" R- S1 M+ |9 E" }
Preordered sets$ J2 @& @9 }6 ~' c4 K
Priestley spaces7 ^8 u# D! ^3 J$ V( u0 S; g
Principal Ideal Domains9 Z0 w# g* D. n2 B- V3 k
Process algebras( g& t, U4 [8 A& n' a$ G
Pseudo basic logic algebras
) @5 L- ^, ^$ Z1 EPseudo MTL-algebras: n: o) d% a% ]. J3 Y
Pseudo MV-algebras
( m' p' h& [3 L" S+ [7 M5 H y* KPseudocomplemented distributive lattices
+ g F5 |) ~1 X; \5 hPure discriminator algebras0 T4 N6 K7 P* L5 f2 S& V, \6 z. V
Quantales
9 O3 P+ Y% J% Y Q, C, ? sQuasigroups/ O! w T# m4 o$ v
Quasi-implication algebras
- f" W" N4 U: D4 @Quasi-MV-algebra/ _4 H3 d: f) p" A) B
Quasi-ordered sets3 W- |6 c' {# j& I& h- \
Quasitrivial groupoids2 I' W" J; I9 S2 c8 [, ?
Rectangular bands$ E+ y( o6 x2 h; ]
Reflexive relations
- }1 l! r( Y s m% j1 @Regular rings8 H3 I9 s( ^# `. b. Z
Regular semigroups
' ?4 p& u9 R: g1 p, yRelation algebras
, _+ q% o( G' V" J& s9 jRelative Stone algebras, f# P+ {5 ^; z" M' `; M1 w# F
Relativized relation algebras
$ R# h! q; x7 a4 H) k0 Z: `Representable cylindric algebras% G' c$ x3 c" m; S$ r5 T7 B
Representable lattice-ordered groups
$ W X0 s" S& B2 f4 XRepresentable relation algebras
0 P2 t& x6 l; l6 O6 `Representable residuated lattices
! i: K% [0 n j: C; p& C9 G' UResiduated idempotent semirings
! H4 F! V J7 T m9 t6 r8 SResiduated lattice-ordered semigroups
, @! R7 f6 f# M3 { V: Y* MResiduated lattices
+ J' y. ^' [! i# Q M# JResiduated partially ordered monoids
% S9 v8 s" _" j; U- VResiduated partially ordered semigroups6 b, h C- Y) I4 J! D- H
Rings9 L7 O7 J* T7 n& b
Rings with identity4 u3 C. ~/ r3 E
Schroeder categories' ]0 c2 v8 @. T* j+ m0 U
Semiassociative relation algebras
+ S/ d% M% c( ?5 l- X6 DSemidistributive lattices6 ^0 o d# D, g d3 E
Semigroups, Finite semigroups
! v8 H2 S5 \$ {6 ]Semigroups with identity& d! ]! U5 f* k j2 d6 @
Semigroups with zero, Finite semigroups with zero, r0 R2 v$ v1 _. n' I- a' m
Semilattices, Finite semilattices$ B6 f5 N" T8 r$ b: {
Semilattices with identity, Finite semilattices with identity
9 _; H. s; x H: s5 {5 G wSemilattices with zero
% o9 w3 K$ t9 U: ~6 M8 HSemirings
3 V( i1 t; {" V/ Z/ oSemirings with identity
4 Q) c9 E2 _: G+ g8 t- H* SSemirings with identity and zero8 R# O! B$ E6 w" T
Semirings with zero
4 V' f6 g( f0 hSequential algebras) X" _& b! m5 Q- S. T, ~0 A2 f0 q
Sets
! q1 q; |8 G, X2 {: FShells
9 f* [& T' U% X; a1 l1 ^Skew-fields5 K/ o. ]9 Q8 s8 \; H
Skew_lattices
5 T* h8 x' f; C" g" M% Y% SSmall categories! X/ f$ d+ z ]- h" {
Sober T0-spaces
3 T: V/ r1 @+ |$ K% C vSolvable groups
& x! x; C+ ~, v- Y9 ZSqrt-quasi-MV-algebras
* h7 t+ ~" T4 U' Y7 a! pStably compact spaces
# @7 v7 x( C. L, @) kSteiner quasigroups
2 L/ d! S( D8 j2 gStone algebras6 ^; R$ J0 d% @4 P5 M/ i
Symmetric relations% W3 U) S! a T# k- B- s5 w
T0-spaces
6 X4 B6 B$ e& q# B/ \T1-spaces
# c& S. f5 w2 j) G @) vT2-spaces0 i; d1 u: `$ @$ M5 S
Tarski algebras
& b. c# _3 f+ O4 r" sTense algebras
' i5 z5 i. a% {3 l; \Temporal algebras. @" x; O% J% Y3 J
Topological groups
/ O) [$ m1 v! E. T5 UTopological spaces2 a/ u# b/ r* b1 o1 f3 x e2 U
Topological vector spaces8 I( b; X( e6 y0 w
Torsion groups
! K# t4 P; v$ l4 s& K6 f. A6 STotally ordered abelian groups/ R% V/ ]5 x4 S% F
Totally ordered groups% s j! W, V3 v
Totally ordered monoids
9 r3 e! o$ y3 W7 w3 ?* ?8 W: ~Transitive relations
) x5 x' V3 u% ATrees$ w6 K8 d# ?* f8 d1 G( G5 q
Tournaments
+ A" O5 s9 C. _Unary algebras! C- |- V+ j+ E( p
Unique factorization domains
+ c/ M* e! M" l% A" S: [Unital rings7 d# _+ M7 N9 m6 k) Q; }- Z
Vector spaces5 f- i; S, D. D% U" d6 t+ ^4 t; H$ _
Wajsberg algebras+ r- M# F9 d0 a @
Wajsberg hoops
- v" P9 H! s$ M& h6 r" `) \Weakly associative lattices( {" }, s) H& ^2 \8 F& ?. L9 X; {
Weakly associative relation algebras
, \# l" r1 Y: \+ f/ U/ v8 ~Weakly representable relation algebras) j# I' D n2 x5 y
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