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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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( x" D3 L1 ] y+ C
+ |5 ^/ u8 W% \5 cAbelian groups Abelian group
: ?/ N* o5 a9 H8 iAbelian lattice-ordered groups$ [# C3 N2 X% A9 T
Abelian ordered groups+ X! z6 H8 ^, {7 D
Abelian p-groups0 P% n% U/ N( x, n9 m
Abelian partially ordered groups
2 a! @/ b& c( e; `, R. zAction algebras Action algebra( s: K( g6 ]3 Z: \* V' g. y2 X6 g
Action lattices1 [ K( Z, X4 h7 A# l
Algebraic lattices
4 T: j3 @: {! ^& ]+ J8 p3 c; I, BAlgebraic posets Algebraic poset. F, q5 O' j+ G) L* Y7 u* w
Algebraic semilattices
m8 r$ `2 y0 ~8 t6 f! ~$ ?Allegories Allegory (category theory)# X8 i2 R" e2 ]# K/ i7 \
Almost distributive lattices
5 I9 O! n* B. U' s( Y+ jAssociative algebras Associative algebra3 W& \6 Y" k9 ^
Banach spaces Banach space7 |/ Q) `, \6 s$ G. `" q! |* d: W* Z
Bands Band (mathematics), Finite bands
( Y% T. B8 U/ n2 eBasic logic algebras
& r5 z( c* W2 B1 ABCI-algebras BCI algebra. {! q8 M9 R; m @
BCK-algebras BCK algebra2 a* \9 F2 G9 ?) P: _
BCK-join-semilattices
- y! q& d1 d/ C! HBCK-lattices
" |" A: `# S" O, u7 B/ ABCK-meet-semilattices# e/ x' k3 D1 h* O7 q( g
Bilinear algebras
# `8 n6 e, ~2 w$ i4 w* |- j+ DBL-algebras- n5 p, `$ C; S: G
Binars, Finite binars, with identity, with zero, with identity and zero,
+ d1 d& v% x% \9 gBoolean algebras Boolean algebra (structure)
+ E- ? i9 I& q, QBoolean algebras with operators
" m7 W9 a- p. q# WBoolean groups
7 J1 E, `! b2 V; NBoolean lattices
# a# R, g% b1 R6 V) d# u, s9 m* yBoolean modules over a relation algebra
4 K) _0 g" \% }: u6 [& hBoolean monoids! w3 @: ^ U8 o+ D* F
Boolean rings
3 m5 M3 u& \) s& KBoolean semigroups' t) [. L7 h. C: H) b) Q3 h
Boolean semilattices
- H+ V# U1 y8 C1 L2 YBoolean spaces
/ M" V+ w8 X3 q" O! V+ P0 \Bounded distributive lattices
2 n0 e% i0 h& A2 \$ P; Q. ]Bounded lattices; c4 W, y5 t( T3 Y* w! z6 s
Bounded residuated lattices5 [! e6 g( D1 R R: z- S
Brouwerian algebras! J' }; b# m' i6 e; k6 x; v
Brouwerian semilattices
8 ~1 e) `/ v. Q! aC*-algebras
* y, r6 S" q& QCancellative commutative monoids) D6 _9 a' a) f( s, q! J8 g
Cancellative commutative semigroups2 u7 {& r; e( A( k- S" p/ @$ z
Cancellative monoids2 v9 T/ f8 _6 n/ O: E/ T4 Q+ r
Cancellative semigroups
7 M" i: R8 P' t q- _; PCancellative residuated lattices, Z( O- Q. Q1 q7 B
Categories6 C6 z; o9 ^2 Z# \& c8 f, U% Q' w, K
Chains
8 M/ ]) n$ V5 U0 Y$ a$ T0 [Clifford semigroups3 p5 v* H+ w, S
Clifford algebras
4 W+ c% Z. T3 Z% r: X* OClosure algebras
; p: B4 q/ E0 ?Commutative BCK-algebras
: n5 q0 ~) z: D, ~Commutative binars, Finite commutative binars, with identity, with zero, with identity and zero ( t; N1 B5 h4 h7 n, a8 Q( D$ q6 Z& h
commutative integral ordered monoids, finite commutative integral ordered monoids9 x1 ?, t+ L# e, T9 n$ y
Commutative inverse semigroups/ C/ N8 f) a* ]
Commutative lattice-ordered monoids
/ _) W+ f: B' f8 j; h# @Commutative lattice-ordered rings' C1 N) O; o8 F! O
Commutative lattice-ordered semigroups- f: ?9 I; k" Y% z' |
Commutative monoids, Finite commutative monoids, Finite commutative monoids with zero
$ w: @5 u* L* `: R0 vCommutative ordered monoids" ] @: N# B3 n$ j4 @* p% F. O
Commutative ordered rings" _6 a! {! K- A3 |6 h
Commutative ordered semigroups, Finite commutative ordered semigroups5 I* Y0 y# E" r# V7 m4 U- p
Commutative partially ordered monoids) \2 h5 Z/ s- `$ M/ r
Commutative partially ordered semigroups
; v( v8 t$ i) G& I; mCommutative regular rings
1 i0 I' s* q6 jCommutative residuated lattice-ordered semigroups& u! w4 K' ]5 N. N: |8 n+ I4 d$ Q
Commutative residuated lattices0 r0 n9 D7 K4 G4 b3 Y/ r/ f
Commutative residuated partially ordered monoids
8 v4 n9 P. D& B( O, FCommutative residuated partially ordered semigroups
5 j& Y9 W4 C2 k- J- ?. H2 z9 ?& ]Commutative rings
V5 v4 r0 w. r- W" V9 NCommutative rings with identity# ^6 F3 \0 \- B4 j5 C
Commutative semigroups, Finite commutative semigroups, with zero; U) }* K3 Y% [( l
Compact topological spaces; Y# D/ c4 W: a
Compact zero-dimensional Hausdorff spaces6 P! o' Z! }: E' p) {; I# g
Complemented lattices3 f# _9 u# g& z) J
Complemented distributive lattices/ n) }; u' U9 a- w+ R3 d5 T
Complemented modular lattices
. l8 k& M7 ^& @! P A' @Complete distributive lattices [* h8 K. u, R. [
Complete lattices9 @& }" D" B4 I
Complete semilattices
1 H" I' c- C5 |0 v2 G& fComplete partial orders
+ W& R; ~* Y ~* E) T9 d! U9 KCompletely regular Hausdorff spaces
. O! P# }8 O% n8 T0 O1 JCompletely regular semigroups* N& @) A; B3 o: i6 D2 v, k
Continuous lattices3 X+ }# C8 U3 c `3 C- y% c& ?
Continuous posets
8 m0 ?; A7 m) K4 c( i2 {* rCylindric algebras
" K7 F" f$ \9 M, qDe Morgan algebras
' j! U ?* U. J) ADe Morgan monoids y. Q) r- q) b3 r
Dedekind categories! C' x+ t- A1 z* I% J
Dedekind domains4 k4 {. |( F7 P) j
Dense linear orders
- }( R3 {5 D7 y6 L+ G) HDigraph algebras
+ c4 K2 k/ Q' k* n3 g& L; w9 ]Directed complete partial orders3 N6 K8 c" T) F, w+ k5 C
Directed partial orders
' I8 H' o5 _, e& jDirected graphs7 g$ e! W1 g* w) @
Directoids
6 N$ r7 I; D3 |) q/ JDistributive allegories* e, |" ]" S3 @5 z" j& ^
Distributive double p-algebras B& G* @5 B6 V! M' j
Distributive dual p-algebras
* h) `, b; S" b: a- {Distributive lattice expansions
; M( t \# t: z5 q3 w% wDistributive lattices. Q2 i# I9 q9 i
Distributive lattices with operators" N5 Y3 g r [8 [- Z9 o
Distributive lattice ordered semigroups
5 S4 {0 k0 Y8 Z& A8 a/ O# n1 j( CDistributive p-algebras2 I4 |/ F) Z3 }" x
Distributive residuated lattices
/ `7 }. E, U$ j/ w- V' y% z; yDivision algebras' r! {( [% P, Y! D: x
Division rings
% n8 r6 x! e+ B0 T4 c$ u8 UDouble Stone algebras8 J) h* U9 M# I& p
Dunn monoids: E3 r* N5 I, B. W& U
Dynamic algebras
* @0 \6 a7 q8 x4 D( r6 d3 V9 h0 }Entropic groupoids$ J5 Y' X4 S _
Equivalence algebras$ q" @$ F& O5 n+ w1 {
Equivalence relations* z8 x: @! Z( ^5 B7 T
Euclidean domains
% q: I* S8 k+ d, M7 E8 |3 j" X* Hf-rings R+ E8 N9 ^9 t# d
Fields5 @4 A) o9 {' t" K
FL-algebras4 K$ c) w" E* T3 j
FLc-algebras
0 x" A+ x I2 p/ i; |) @FLe-algebras0 u/ k3 }8 _1 t; @0 E7 P% U9 j
FLew-algebras
/ y6 p$ t/ `( E+ `3 }' X" MFLw-algebras" m) i u( h, Z* [! T5 _% R# I
Frames
Q: h: G7 w) IFunction rings
3 }# P c$ R' N* ?/ C0 \ }$ g5 p5 oG-sets
: p( [6 p& G" R& ~2 X rGeneralized BL-algebras- ?! a( M& C1 t" @
Generalized Boolean algebras
3 g* s5 b, f$ V, ZGeneralized MV-algebras3 ?! Q8 k: W3 t7 J' z3 D ]% A+ R. f
Goedel algebras/ b- u: g, h! A6 {8 Y# h* ]
Graphs7 ?& b$ P: A1 ?1 @ i9 I
Groupoids
* g7 }0 z: Y( ^4 cGroups7 W, l2 i* \% u, w. o
Hausdorff spaces
# I: h/ g/ r6 @0 J! |& LHeyting algebras; H8 w- Y* l/ K" n0 X3 X' F
Hilbert algebras
& B1 w5 l- f) g; X9 F, e2 rHilbert spaces
' N( s+ C# L' [$ _, THoops2 _% X% k9 q& t/ D0 s; t
Idempotent semirings' `4 k, }7 g& T# z. h3 a
Idempotent semirings with identity' [" Z9 W6 T0 j
Idempotent semirings with identity and zero/ O- f1 u4 o7 ~) d, [% K F
Idempotent semirings with zero
- ^7 U* x( }' M& O# xImplication algebras
$ p' ~7 q- k" g$ xImplicative lattices2 k; g5 E" W# [8 {
Integral domains
j- V; g* ?, I, S( O& MIntegral ordered monoids, finite integral ordered monoids
. B, n( d6 G: b0 x" x; h/ P1 ZIntegral relation algebras
0 p/ M K5 w2 M+ V$ o& R9 QIntegral residuated lattices
9 a( U$ ?, ?& K# tIntuitionistic linear logic algebras) L' L# |: X. {( `# ~$ v4 P
Inverse semigroups
$ _( t1 b( K- a" NInvolutive lattices
$ V8 F4 I, u1 c, d* K# _Involutive residuated lattices. y' a( G3 W" y& j# B! J( z
Join-semidistributive lattices ~ E' @9 f, m6 P) b. X* e$ Y
Join-semilattices/ I: ]1 Y' ^9 w9 V! A% u2 B
Jordan algebras
; k* v; J. j6 ?/ f; e) K- r- T! A6 ]Kleene algebras$ T# K# G6 W+ i+ I; ^9 x f
Kleene lattices* l; S. K# M1 ?' ?! X* V
Lambek algebras
( P- ~$ Z1 Z* L3 ^. p3 t3 A* q/ CLattice-ordered groups# v# T8 V A, J* p" L b
Lattice-ordered monoids3 H" t. Q G6 x* z. i0 B: f C
Lattice-ordered rings7 k2 m. U- L3 i/ \; b& q8 G
Lattice-ordered semigroups
1 C( Y2 w. n5 E3 r- |Lattices
: c( k7 d! z' F' u' X) oLeft cancellative semigroups
0 I: t* s8 ]: Q1 `# u+ u. zLie algebras
' ]7 l- H$ g5 H0 W. |) J/ H" n: tLinear Heyting algebras
, f4 _+ M- P( B8 u7 \Linear logic algebras c( ?8 y, V9 ^, A( d* h
Linear orders
( W6 d5 P! V3 P7 q. w- ~: K' v: tLocales
2 i) t' z1 e- T+ LLocally compact topological spaces
( R- L% P7 y9 g7 hLoops' e6 } {1 ~ Z7 m% w O
Lukasiewicz algebras of order n
$ r3 B* a+ I8 Q1 f7 nM-sets7 f. T" x- V( e; d8 P
Medial groupoids
: x5 O0 d" p8 d2 k1 G& m2 dMedial quasigroups9 M$ z: _: e! j# Z. g+ h8 R
Meet-semidistributive lattices+ M8 D. i/ f: y
Meet-semilattices/ f7 s* W, J6 v0 H4 H+ r) p
Metric spaces
' n8 w; p& k9 P3 B$ _0 Y/ lModal algebras
0 D2 }% l1 M1 n" }- P; rModular lattices7 l. {' c" i0 r* \* W
Modular ortholattices
! U Y) \. W4 k% d) s4 sModules over a ring, |1 Y( K' r6 w6 z
Monadic algebras- W5 a5 R7 E0 \) d: b+ @, I
Monoidal t-norm logic algebras
$ ?1 C4 e$ l6 B- C# tMonoids, Finite monoids, with zero
8 S" O% z" A% U3 q9 c$ x2 Y9 B( SMoufang loops/ T1 y' J5 t* C- q
Moufang quasigroups. b7 [+ f7 C1 \ c$ y! A- R: @
Multiplicative additive linear logic algebras
L; E: P5 D0 s9 k$ F. k4 d: JMultiplicative lattices
) h/ G) l7 o+ h/ H- R, W0 z! f; XMultiplicative semilattices
x* U1 x# o+ _: B! NMultisets
- w! X; M/ W2 S1 cMV-algebras4 ^1 Q0 o; Y- }+ F
Neardistributive lattices
* e: t& U2 s4 z. pNear-rings
/ r. ?) B4 L$ T& l6 ]3 n7 T4 }Near-rings with identity
( H5 Z; \( K; e( iNear-fields
5 Z0 _: h% v% v6 x- B5 x2 r& l& gNilpotent groups8 D0 k, J% _( Q) J
Nonassociative relation algebras
7 s4 b) g6 T* a+ C' o2 Y% A/ F5 C( hNonassociative algebras
: A$ y6 z& b& y9 j+ D kNormal bands
7 t4 o9 f9 ^* ]Normal valued lattice-ordered groups
( A. f' H! C' O6 g' |Normed vector spaces$ {' K% E. B/ v ]9 ]
Ockham algebras
3 B" L: D# ^0 s$ _1 uOrder algebras
$ L9 S) ^! T% v; f3 X R- Q% \0 DOrdered abelian groups1 U* X- b9 v. [( J0 P5 e
Ordered fields
/ w! V6 z8 }- V, O9 C9 b$ {) w2 cOrdered groups
4 d' I. g& d3 o- E2 vOrdered monoids4 T9 |7 c2 i3 f" w
Ordered monoids with zero" l4 D2 q7 R6 B* y6 ?
Ordered rings
& Y% T. E; k+ \' p6 z' dOrdered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero
- _5 v9 S- c2 U" W0 EOrdered semilattices, Finite ordered semilattices% \2 ^6 [# X3 [& } t
Ordered sets9 }( S; P& S' [( d1 r
Ore domains/ ~* h# i, O% e- T% y+ @- a8 J( Q+ M7 C2 |
Ortholattices
+ `& v; Y) b' Y1 T3 n' ROrthomodular lattices* ?7 K+ e8 b% t5 p. S
p-groups
) C/ ~( p! q3 vPartial groupoids5 M5 y$ m3 z# E- f# ^( n4 T0 y
Partial semigroups
) `4 p$ \9 B, v% _; h# gPartially ordered groups$ G1 p+ `8 f. K$ s6 g4 S+ J4 b
Partially ordered monoids
" k }2 `9 L2 [, ?2 A% C1 rPartially ordered semigroups1 b% g8 U! T4 Q+ V5 H5 r2 d
Partially ordered sets8 C6 e- z1 `$ a3 K
Peirce algebras: ^7 H1 L; p+ G! q, g! _! \. Z
Pocrims6 R* q/ G) Z2 U5 R/ U- @
Pointed residuated lattices
/ a1 s$ z7 O6 |Polrims2 P/ o/ K# S( [
Polyadic algebras
0 g9 H F- J j" R# Q2 IPosets$ K6 f( H3 P7 F1 p
Post algebras
! N! O8 p0 w' J8 {8 R7 CPreordered sets
: J- k: N, D4 }- C/ _7 H: CPriestley spaces# k% J9 |' j: q3 _+ R$ ]! i
Principal Ideal Domains* n& {" E7 K% V, r
Process algebras
2 B( [3 @! m: o- HPseudo basic logic algebras9 ^$ H4 w a* E' o) r5 A( n6 E
Pseudo MTL-algebras- z6 I7 ?# M# j- ?+ n
Pseudo MV-algebras$ v4 n6 g8 Y2 l; K0 E+ p3 }7 C
Pseudocomplemented distributive lattices
8 Y" P& w4 v1 Y0 VPure discriminator algebras8 ]0 \' C+ a* ~. R# C( Q: T$ }7 D
Quantales
# Z! I: ~. ~2 ~0 ?* z& dQuasigroups
0 k ^9 P+ z* i7 u; zQuasi-implication algebras
3 N/ ?' m2 ^) gQuasi-MV-algebra
, u5 X4 A" c! T5 @2 H4 |1 [Quasi-ordered sets
: c$ A. B+ \% W- I! o5 O {8 ]% ?' VQuasitrivial groupoids
8 g; X2 w" H4 c. v0 I1 HRectangular bands6 T; O, \- F! M8 D6 U0 y, b
Reflexive relations
5 x& e/ W5 _# K }Regular rings
2 {) K1 H0 s! S# URegular semigroups& t# o% ^/ ? r* M
Relation algebras
. {. P( F4 e8 K- D5 V, ^2 xRelative Stone algebras
$ X# m2 J J* h$ w, h3 N" yRelativized relation algebras
7 Y& _: {0 m, k0 ? [Representable cylindric algebras
! K+ N% m/ Z$ D' oRepresentable lattice-ordered groups- W K! b7 ]' B; {0 P3 R
Representable relation algebras
$ N- C8 f7 `7 v5 bRepresentable residuated lattices
: n' a9 Q8 P! I; Z9 M0 W; mResiduated idempotent semirings
8 L6 @+ b6 `; vResiduated lattice-ordered semigroups7 Y. {& Y1 _* }6 c/ y- U
Residuated lattices
1 {/ F3 s, W% r: ?1 i$ X% @2 u' HResiduated partially ordered monoids
# ]: p O( U8 l6 y/ PResiduated partially ordered semigroups
2 F( Z: W* e- {Rings0 Z& p# D2 ~7 d0 M
Rings with identity
6 o# X) I8 p* |Schroeder categories
8 C7 S5 w6 o3 j3 [4 ~# KSemiassociative relation algebras
6 K- t7 y4 T ?' U. I6 uSemidistributive lattices
6 c3 t0 u+ s- Y; ^' u9 h1 ?Semigroups, Finite semigroups
8 r* l# S1 P' e, m1 FSemigroups with identity; }, H3 ]; t& f5 V) p
Semigroups with zero, Finite semigroups with zero/ V+ N& r9 H, h4 V1 G+ ?& E [* w
Semilattices, Finite semilattices
9 l6 i2 c/ G" X& m0 z$ G! z- g/ DSemilattices with identity, Finite semilattices with identity& r+ B7 v8 t) J; E( l8 @! l3 F+ j
Semilattices with zero
! G1 B& L; H! [9 o5 D7 SSemirings
* m, \: Z6 P6 }: v. b A1 I6 CSemirings with identity
Z( j8 J/ B" J2 N7 d: L/ p2 BSemirings with identity and zero' S. e$ B) O' B
Semirings with zero
% ]4 A) S* ]9 u. GSequential algebras" x# Y* `. t& d- c
Sets8 i+ U) }( X8 p. b
Shells2 Z) H2 B- K$ l0 F6 d& [1 k
Skew-fields
0 o6 X1 J1 X/ R& w' ]Skew_lattices
% Q+ U) v9 b ]4 ~3 ?8 E5 ]Small categories- r p4 X5 o4 D
Sober T0-spaces. a. Y5 f8 ?9 V8 w9 T4 I# A
Solvable groups
) m6 s+ U* v9 b- {Sqrt-quasi-MV-algebras' [# v, Q# s% {5 q- j$ V7 P
Stably compact spaces
% ^; ^6 e; k2 C4 ^Steiner quasigroups
! n( I; B' U# W. i" ?/ ]Stone algebras* `+ d. o* N" {2 o$ V9 z! q
Symmetric relations/ D5 e3 ?7 L0 O/ Q8 o8 J; R+ u% K5 i
T0-spaces
( d7 w6 M9 s" NT1-spaces) T( n+ x- s8 |; W; I$ T
T2-spaces
+ ?* z$ V9 i2 Y wTarski algebras! X. y8 g6 r- c
Tense algebras; B1 S7 x0 W: Q0 m1 V* d
Temporal algebras5 P+ O3 x' U$ b/ V& P
Topological groups. k! l% s9 O' b9 R: c9 e4 _, h
Topological spaces& C1 g1 C! Q0 B# J- B
Topological vector spaces7 K0 o4 {7 M3 Q! v: k: \$ S
Torsion groups% e6 E5 D5 W6 Q2 e; i% V: }
Totally ordered abelian groups
( Y& G+ h8 Z0 o7 X9 \/ lTotally ordered groups# X6 V9 ~5 {: B( Q5 ~9 m
Totally ordered monoids1 J+ q6 q# ^$ d5 D; x; \
Transitive relations' B S. O- m9 r! B7 m
Trees
6 Z5 S" d& _/ d- D+ zTournaments
( r. ~# a7 v) M- h3 dUnary algebras i) u; i" \ K4 }# c* [
Unique factorization domains+ H* j5 D- G# i' j" K
Unital rings8 {+ Q1 i2 m; P- z1 ^; K
Vector spaces
8 f% d; l& h* bWajsberg algebras
3 X( k/ b! t( Z( }5 zWajsberg hoops Y; T, h# p! v7 E. J
Weakly associative lattices
# R3 g0 A A6 e0 S0 k$ O) GWeakly associative relation algebras
0 Z7 L. V9 V8 B' C& vWeakly representable relation algebras+ Q& [5 n9 F. s2 [6 z2 }6 C( B
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