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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$ W; t- b) a0 U$ U3 I) P) w! o9 ~. D" F
Abelian groups Abelian group
1 w8 y, X8 L) ]4 Z9 X! TAbelian lattice-ordered groups( d) a0 q7 W2 a; f/ H" S( G
Abelian ordered groups
2 Y' i& S2 v# ~: g0 mAbelian p-groups
+ s8 J, |0 \& |, w+ X3 ^. yAbelian partially ordered groups/ h# n; T' N( Z4 d" i! [* [% n6 E
Action algebras Action algebra
" w$ h& O4 a8 j n. f/ W* }Action lattices6 T9 Z! H+ |2 s$ u
Algebraic lattices0 k+ w# x, B$ y5 j5 r2 M
Algebraic posets Algebraic poset; \9 a0 v2 F* s" L) r* b
Algebraic semilattices6 u) R8 t; w# d6 Q j- s
Allegories Allegory (category theory)# c. w7 L- \9 i9 r
Almost distributive lattices+ r+ O3 [+ b9 A- S# J% {$ T8 C0 h
Associative algebras Associative algebra
7 ^: n: U6 z: i; H* }5 M* X$ B FBanach spaces Banach space
& y; j6 i& w# YBands Band (mathematics), Finite bands" }+ g6 { T) r, S2 G
Basic logic algebras
. Y/ \6 U; R6 N+ ]) {! `( w6 YBCI-algebras BCI algebra
4 ]6 x* y( t$ o6 YBCK-algebras BCK algebra. W" w9 a! c8 R: Y% Q9 T$ J
BCK-join-semilattices" x0 o. i/ h$ o( c7 @9 u9 E
BCK-lattices9 ~0 D$ I* ]5 z' d
BCK-meet-semilattices) e# u3 Q5 E8 U/ ]: B
Bilinear algebras
0 v, a- b2 p7 ^+ o- VBL-algebras
" M" B7 J" S# ^: R XBinars, Finite binars, with identity, with zero, with identity and zero,
, t# p' v# ~6 hBoolean algebras Boolean algebra (structure)
0 w S; J6 q4 {Boolean algebras with operators! H+ M' J9 q; h( y- O! s: m
Boolean groups
2 h3 m( {4 ? Z+ E8 x& r6 \) O4 j9 zBoolean lattices/ Q* h) Y, C) B2 f' `# M6 ~
Boolean modules over a relation algebra( |. p$ m6 f: B" J; q. e0 P5 ^
Boolean monoids
) N, y9 |6 G: {$ _; w# oBoolean rings5 |" x [2 X2 `. |/ d- c+ M
Boolean semigroups
: {# O/ @: R: _3 W* l. ]Boolean semilattices' |" K# x1 I$ f( J; b
Boolean spaces7 A5 C' d2 I6 g- L2 \, h# f, g3 o7 N3 I
Bounded distributive lattices9 H$ }( k4 y, ?
Bounded lattices
5 @7 t- m! T7 O8 `& i- kBounded residuated lattices
* g" r, x# q2 R, J1 ^' Y6 ]Brouwerian algebras
* `4 N' h' V" r9 P5 TBrouwerian semilattices
; A% v7 `0 [2 _% e% P3 |+ oC*-algebras
: m4 l/ ]9 U9 U6 dCancellative commutative monoids
( L8 L6 Z$ U' B- B* C, A$ aCancellative commutative semigroups0 X$ u5 r7 x6 E g A
Cancellative monoids
. A0 q! J. g3 O5 U. QCancellative semigroups
7 X. h6 O7 o1 l" g$ zCancellative residuated lattices
1 ^$ u1 E5 O$ ~% [7 S( eCategories
* v' d2 A$ R4 S8 D% }Chains9 F- w; {) ~$ v7 u9 g3 P
Clifford semigroups
) l, j8 A8 y) aClifford algebras
1 X5 I9 x, [) {9 \Closure algebras
8 w- [3 D `% D- WCommutative BCK-algebras* a" ]" m1 `, b/ F. {$ X1 K6 X' E! H
Commutative binars, Finite commutative binars, with identity, with zero, with identity and zero 2 f6 f7 P' a3 |2 D) A4 W7 }- @" a
commutative integral ordered monoids, finite commutative integral ordered monoids: |+ f) `- a# d7 \
Commutative inverse semigroups5 e1 M! n; P# M+ @& V
Commutative lattice-ordered monoids
: @ I) @# F" bCommutative lattice-ordered rings5 p9 F( Z# y8 i
Commutative lattice-ordered semigroups( w; n& z+ G/ n4 a/ [* J( t+ b
Commutative monoids, Finite commutative monoids, Finite commutative monoids with zero
% F, u$ l( V* r$ \; p* @Commutative ordered monoids
! y6 w' s: e& }8 BCommutative ordered rings& {+ ~, D5 x' G+ o" E* R4 ~" L }
Commutative ordered semigroups, Finite commutative ordered semigroups' J, J+ B1 N1 P' @1 u
Commutative partially ordered monoids8 S$ M x% \9 A! }6 G1 l
Commutative partially ordered semigroups
& h: }5 A3 ^( U8 jCommutative regular rings. T( |" ^3 \! I M1 _0 t
Commutative residuated lattice-ordered semigroups
4 D2 H% [, p7 W9 n$ z; c5 hCommutative residuated lattices3 W" s2 A% e! `: y+ k
Commutative residuated partially ordered monoids" C% r$ ~2 [! o) c4 z
Commutative residuated partially ordered semigroups* m1 s. {1 _# H' \; O4 W
Commutative rings7 C3 U o/ }& i4 ^
Commutative rings with identity
2 u' M0 F1 x$ ~" p% }Commutative semigroups, Finite commutative semigroups, with zero
- a! J6 H+ W1 |- e UCompact topological spaces1 g6 i2 j, p3 w% q! l; a( |/ i
Compact zero-dimensional Hausdorff spaces
! _4 f5 z! ]: C8 H: [Complemented lattices2 {- B+ \ Q- ?$ B
Complemented distributive lattices. F5 o2 M @! I2 |- C* G$ v
Complemented modular lattices) N0 i- k, O2 a+ r& @, K* l9 k8 s$ f
Complete distributive lattices, d1 X% Z# y1 u' @
Complete lattices4 K, e: p, g, y3 d
Complete semilattices
3 a$ d$ m3 [! d0 _! iComplete partial orders6 I) f$ [6 \; a8 N C Y7 z
Completely regular Hausdorff spaces
$ E3 B- W# }! L# ^3 z# O7 G7 A0 dCompletely regular semigroups9 }: R* U5 o4 P8 r' d# Q# Q& |
Continuous lattices0 }% M8 w$ K/ X! d
Continuous posets3 y+ g0 K* a( |8 z
Cylindric algebras) k& v0 {% U" ?: `* Z
De Morgan algebras
. l# B& K4 e/ _, o2 O, B# sDe Morgan monoids, b9 J f% i( X* A$ {* B3 M# d
Dedekind categories9 C5 i) \" X6 C, m8 N
Dedekind domains
* }- v+ A2 b* H" EDense linear orders S* }6 t1 k3 F
Digraph algebras8 J3 A9 U4 {5 Z3 z4 r1 D
Directed complete partial orders
$ `" f7 h, e4 V0 d9 D0 NDirected partial orders
, b5 }' E# `, a5 MDirected graphs
4 D" m* W2 P8 a- a0 PDirectoids
0 f& P) n" g" Z9 h+ a! I, x1 }Distributive allegories
' u2 q9 ^3 Z9 T# L6 {! q/ `Distributive double p-algebras
2 G- `- ~2 ~ c4 d' H$ D5 Z5 qDistributive dual p-algebras* ^3 k' F( N; t+ ]. ~/ S9 q/ @
Distributive lattice expansions
" E: Q' t6 _3 Y' ~Distributive lattices
0 B: D7 P1 `( o3 m) tDistributive lattices with operators/ r6 M1 X! V9 T& B' u
Distributive lattice ordered semigroups# W% ]; R J4 {. \0 {# f( O0 [( w. J
Distributive p-algebras
+ s+ _, Z7 I9 B+ t* f. k6 {Distributive residuated lattices
3 n, Y2 W9 x$ `% {Division algebras
0 |, ^/ T& m+ ^( aDivision rings
8 l* d7 d3 s) l* L5 b; NDouble Stone algebras% l& o: ~. }- |- x0 G
Dunn monoids7 x5 L) W0 r" v/ X6 P
Dynamic algebras
6 D- z3 _1 a9 ZEntropic groupoids
) |5 D5 X0 J8 Z& ^Equivalence algebras
* z: [6 G7 G$ @/ U9 F; v$ sEquivalence relations
2 [3 p5 e6 Y7 }+ ]3 yEuclidean domains+ F1 `3 M, L% z) ^. _$ M4 M/ g
f-rings
f, e9 k/ Z7 [0 [: I$ H/ oFields
g, m8 B- e% l; t, eFL-algebras& Y& p. e/ _" w" b, Y9 J' H: K; x
FLc-algebras
+ O1 v! D5 p2 YFLe-algebras
: T% Y' ~2 k ]4 i! G! DFLew-algebras7 c$ ~# ?) p% ?# u! f$ W
FLw-algebras& r4 @ b* u( ^, j2 D1 p
Frames
6 m8 z5 e# c) ?6 \Function rings9 b6 Z) p0 @- d, S; q/ t; V: L
G-sets
6 V. c) N9 V" ~5 r# r9 |( u6 zGeneralized BL-algebras* Z9 x5 D. Z2 C. s' [6 ]* v) K
Generalized Boolean algebras
2 j" ]& p# K8 D3 hGeneralized MV-algebras
9 @# \% p8 q& jGoedel algebras& H* V4 p+ n) |% T* y/ m( a
Graphs
5 ?! e9 N; h" wGroupoids8 \+ P9 \: j) s+ ~' j% Q9 |3 Q
Groups( y; H8 X# S9 A4 q# Q
Hausdorff spaces2 P, w, S& O' e
Heyting algebras
/ H3 y7 L- ?1 d F4 FHilbert algebras! U ~+ G8 r1 `# ]! K
Hilbert spaces# @) ?8 q' B& j0 ]/ l8 X- Y$ D% X
Hoops7 {4 c+ J2 L- Z4 p6 r
Idempotent semirings3 x" {& U! l- J! j- z3 j) F
Idempotent semirings with identity
/ R* g) y, ^% F4 S/ \. RIdempotent semirings with identity and zero
) H* v# Y& t# Z- G% u8 V4 J+ DIdempotent semirings with zero! l5 ?" m4 ~5 C% B: r
Implication algebras, A- e) J" f. Z& C
Implicative lattices6 y. ?5 S$ W! r
Integral domains
: s8 O8 ]& v+ j% h$ }0 E9 @+ k9 vIntegral ordered monoids, finite integral ordered monoids/ P9 J* p. P' D' g; q
Integral relation algebras- {7 b1 ?( _% f
Integral residuated lattices5 L$ I$ v1 K* u7 \0 t* I% Q% z) X
Intuitionistic linear logic algebras/ t0 Y0 `* m" L$ ^9 U, Q
Inverse semigroups
\ G5 A3 l9 h% A. E k+ w1 w gInvolutive lattices7 h' W" ]$ [4 w3 t
Involutive residuated lattices/ S c/ ]. w1 i2 W
Join-semidistributive lattices) F: Y0 h+ Q4 {' N
Join-semilattices, T6 ]3 D. N9 ^/ o- u4 I, U
Jordan algebras
8 J9 H( S3 l1 ^* S& A/ x uKleene algebras
# `% f5 U1 @5 ^2 V' |Kleene lattices
2 A+ |" a' b, z; W0 M! tLambek algebras1 j/ x4 e9 v* w3 K. F) x
Lattice-ordered groups
& ?3 j: P" R9 {5 ?Lattice-ordered monoids# X1 ]* m* c& M8 j, @ @# D
Lattice-ordered rings* w. I2 \: Z. ]) M# f
Lattice-ordered semigroups- D3 V9 J0 N' d% Q, }% [( k) K
Lattices/ @+ e, O$ }9 W7 U5 L
Left cancellative semigroups/ D/ ]) X. A% z& ~ Q y
Lie algebras" J; E% k! z. _1 a7 }' x
Linear Heyting algebras
* O% g$ r5 m/ ]7 Z* w3 }Linear logic algebras8 E8 }9 \5 N' q* n( q/ E
Linear orders% S& `" \" V2 q; B
Locales
q+ \+ L- d( Q/ S" lLocally compact topological spaces- g* ~) c& Y Q- s
Loops3 B. I+ b+ P& {- b# v- t
Lukasiewicz algebras of order n. ?2 E g6 b; c7 l
M-sets/ t g" H7 t% n& |8 L a5 r+ N
Medial groupoids
0 N& | [ P7 [# AMedial quasigroups8 D* K1 a6 @. \3 h
Meet-semidistributive lattices
$ c) ^ N; A: |/ lMeet-semilattices
5 v( V/ G0 @) s1 LMetric spaces
- D3 l; e- h; q% j( C9 b. sModal algebras0 M( [' P6 S( V
Modular lattices
# J% p+ w( }8 C, p2 SModular ortholattices
6 V( n/ z$ G" Y, I/ JModules over a ring
0 v$ ]0 G+ l6 G+ ^Monadic algebras% y7 r( G, B+ X0 C* A& n
Monoidal t-norm logic algebras
8 Y) w9 S' Z3 @+ K% R. RMonoids, Finite monoids, with zero7 A' h1 V" r( e4 @
Moufang loops/ y8 p7 Z3 y: z' }' u3 ^2 `: B- k! U
Moufang quasigroups
* G1 N3 @# n' F; H) oMultiplicative additive linear logic algebras5 n9 Z6 w0 O3 G# n# J) U. n
Multiplicative lattices
: ?& h! Z. b1 {' r6 JMultiplicative semilattices
/ R3 b. h2 ]8 C2 x" q tMultisets' [. `; w o# Q. _- X
MV-algebras
( `/ x0 X4 a! LNeardistributive lattices; l* F& U; |% T$ i3 ]6 [/ |- q, i8 t
Near-rings
3 J8 H4 _5 u- a' s+ INear-rings with identity3 d, a, A* k( `. j# v
Near-fields
0 c" j2 \: Q: D* yNilpotent groups
: q# e" j8 q) D" n9 UNonassociative relation algebras) x% n* J ~. G
Nonassociative algebras Q# n6 ^; \. Z U7 i' W7 w
Normal bands3 R* ]! g- \/ w. y( E: X3 B& {8 a* j
Normal valued lattice-ordered groups
) B4 E' l& g- \* {) L- _ |Normed vector spaces
% l5 L Y! B; i" h- F7 L2 QOckham algebras5 E5 N+ p5 Z+ Z% I
Order algebras
% T4 c* h9 a) _3 b8 x6 N bOrdered abelian groups( E' g: s- J3 P8 m
Ordered fields
7 ^' Q: {8 m# s* Q( k; yOrdered groups& b# C8 Y- b- f6 a% p- D/ K% O$ x
Ordered monoids( F* F; a6 d8 X7 B ~5 C
Ordered monoids with zero
0 q0 [# u. p* fOrdered rings( A M# D6 a) O
Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero1 k7 H3 w; e% I
Ordered semilattices, Finite ordered semilattices
f. t: q4 Z* B9 M) z. s' \Ordered sets3 _7 V% z, J0 [" m6 \* T
Ore domains
% s) v8 |4 m( K A. M9 wOrtholattices
3 k9 a3 A4 V& `! q) {Orthomodular lattices
/ ]: y( D; O4 O( a1 |8 H9 D. pp-groups2 U5 B1 n, Z# L% W1 A& ^
Partial groupoids
& n: I( b- o& g c5 t: _! L' t# UPartial semigroups
% m5 `% u, j" d- M. X- \+ Z; w0 xPartially ordered groups" w. c8 M# Y% _- u. ?7 q7 I
Partially ordered monoids
! ?! T5 C( I% G7 N' B9 v0 DPartially ordered semigroups" I2 {/ y h7 U5 r9 e: }
Partially ordered sets
6 }8 h, ?" F q2 j. I$ ]Peirce algebras; J# Z/ Z# b' _9 g
Pocrims5 G0 X0 j7 l6 h k: m
Pointed residuated lattices* M, ]# e Q' z7 e" L
Polrims. @2 c" f/ [) J% a
Polyadic algebras
7 \. h) l8 c& HPosets: m, Y( F* d; P
Post algebras
! Q8 i$ @ R0 k2 s& i) f3 RPreordered sets
5 {, r0 X8 Z" h( D, TPriestley spaces. w1 Y( Q* k7 [4 t1 h3 ?6 a- h
Principal Ideal Domains
! [% C' D0 ^6 I, \6 u2 \% |Process algebras
/ \6 x1 b8 b! |1 D! o+ L- [+ C! TPseudo basic logic algebras
+ Q* Z/ @2 T- E: f0 W4 R% RPseudo MTL-algebras2 @& g, P9 l1 U" L0 N. F+ w, l* Q) Y
Pseudo MV-algebras& s- k# s' S* B& W8 _3 [
Pseudocomplemented distributive lattices2 Y0 e& o) Q* i/ k! D( ~) w/ H
Pure discriminator algebras2 ~$ H5 o. B7 [' m
Quantales
# I p& W' Y$ Y) BQuasigroups3 u; M9 J ^3 |& x0 a) z
Quasi-implication algebras, }! d6 M0 ~9 g6 n# `
Quasi-MV-algebra( @8 v7 Y) g( ?0 o8 c- K# h
Quasi-ordered sets
& t3 B" C) \5 t; GQuasitrivial groupoids8 n8 {/ f: {$ `0 M
Rectangular bands
4 f. o* U( N3 s2 a5 nReflexive relations
# d. x! P: M' M9 y. a7 y) TRegular rings0 Z5 x) w5 w* t1 i) y
Regular semigroups8 }* {% q) t5 e5 [' R
Relation algebras
0 b: L4 h* o* O; V" nRelative Stone algebras
9 X" y" b/ }1 G# H& _7 f' V* zRelativized relation algebras2 Q, V- |' @( s- P+ u
Representable cylindric algebras1 a3 E% A9 R D& n
Representable lattice-ordered groups
& `) @1 {- j9 K% z& ZRepresentable relation algebras+ ?5 K: w% f8 F
Representable residuated lattices! B: m5 ?8 k& S4 {
Residuated idempotent semirings+ S1 `3 K4 h2 e/ `: ~ e, ?/ e
Residuated lattice-ordered semigroups
Y3 J- X. l" I. w4 [Residuated lattices
& L" N/ Q, I# a8 fResiduated partially ordered monoids R/ H6 S; O" ^9 C- F0 w
Residuated partially ordered semigroups
9 v3 ^- Z6 m7 H8 u9 S0 WRings
6 P# s* O% @9 X9 rRings with identity/ v3 R4 U. q! Y0 S$ V
Schroeder categories
i) a: ]6 T5 v. ASemiassociative relation algebras
, w% N' ]2 `1 f* B/ ]/ z3 GSemidistributive lattices
) @% v L! M5 Q# dSemigroups, Finite semigroups. }3 k) ?" S2 p" c$ g# J0 x
Semigroups with identity6 W0 @/ U$ ^1 d h% u, j Q. N
Semigroups with zero, Finite semigroups with zero
/ u" d$ `# V( E8 F/ D6 VSemilattices, Finite semilattices. Y6 {3 H5 A( b6 w& z
Semilattices with identity, Finite semilattices with identity
, N$ S. L3 Z3 C2 t3 R4 L9 fSemilattices with zero* Q7 x' q$ t& d5 f
Semirings5 }: h$ c- v; ~9 b9 |" k x; T5 ~. G' g
Semirings with identity5 x- g) y& l' x3 O
Semirings with identity and zero5 Q' w2 x* L! m# j; m* P
Semirings with zero# S* C2 |* p# ^/ R4 M) |
Sequential algebras
: q: I5 x( h3 D0 JSets
# J8 [; t. z" w6 P, Z* B2 j/ c" lShells
8 L& C9 Q+ S8 r3 M( o) _1 _Skew-fields
- G/ u" L$ s1 V1 ASkew_lattices
! s" _, W9 P/ u' |$ c% DSmall categories
: F9 N8 I; f% x- `, T3 aSober T0-spaces
3 |- [" Q- b k( ?3 Y$ C4 ]9 BSolvable groups1 h) a% w$ {( n( C- N( x2 w% U! ^
Sqrt-quasi-MV-algebras
- w E4 r ?7 ]# CStably compact spaces* P+ d) {% q o( b6 N+ I B" V' G
Steiner quasigroups
$ w9 `" r/ H3 A7 ?* ^Stone algebras( b3 }5 Z8 u$ r) h
Symmetric relations
" E, v; t4 u6 W! u; D2 z* J& v6 PT0-spaces
- K. i7 _$ W1 u' R! Q9 T$ vT1-spaces
# S8 x+ ^: e0 a* u. x+ U- OT2-spaces, {3 c- [; [" X8 d$ G0 V* @8 q y- Z
Tarski algebras) }! [: w: p' L
Tense algebras* }6 V* @, w0 r$ i) L7 S; y
Temporal algebras
7 O, n [! q) _Topological groups+ n, d' f* Y1 A9 P# d4 {* t4 O
Topological spaces
* i# A+ x& y2 Z& V. e3 d! s- MTopological vector spaces
7 d* p2 q: i3 q3 q$ gTorsion groups/ e* |% j# F$ K+ ?! b7 Z
Totally ordered abelian groups7 z9 U' x, \0 ~( _
Totally ordered groups
4 ?- G4 q) m9 t4 D1 w3 e1 `1 CTotally ordered monoids
% s- b8 K' D( z/ V5 n& J6 PTransitive relations8 y# D) b) S) v- |) t/ g
Trees6 s) i, R- u0 { }! L
Tournaments9 O: Z7 t$ Q0 n2 Y E! N
Unary algebras) T5 i2 L9 b% r& ^2 d
Unique factorization domains$ j" M. }# e2 h' G' ^* ]5 Z
Unital rings) n) n. j( W% _: ? X/ b3 E
Vector spaces. q/ Q. Z' k; A0 j3 v' ]; \
Wajsberg algebras0 P+ o. T5 }$ o2 B z$ l0 T7 ^! ]
Wajsberg hoops) n* _% W2 _7 H2 q9 W/ _" d
Weakly associative lattices
9 D6 B6 Q; d/ C8 c. {; jWeakly associative relation algebras
! f7 a( v' x# e9 {6 I' ]; v0 s( RWeakly representable relation algebras, ]2 C% V V. [* O
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