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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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$ v0 l) ^& N8 C* I$ `% UAbelian groups Abelian group
6 J% i9 F- c6 Z( |1 Y! U: fAbelian lattice-ordered groups8 P" G7 B1 b3 }5 N E1 r
Abelian ordered groups
5 A6 W$ [8 R! F1 L1 wAbelian p-groups2 k* L- k* N! i. A. { I4 j
Abelian partially ordered groups
* W8 O) u6 N: N8 Y; D1 b; UAction algebras Action algebra
Q ~6 [9 l" h. SAction lattices
9 J. F& D9 N4 s2 M" X) xAlgebraic lattices
( g. H" f. C$ B' aAlgebraic posets Algebraic poset
% |% l# w+ W3 F# X1 {2 fAlgebraic semilattices; ~ S) V# v0 N
Allegories Allegory (category theory): D; U& S( V$ U
Almost distributive lattices8 U" V3 [( d' C Z/ z8 u
Associative algebras Associative algebra! F3 K7 m! |4 i. B4 E
Banach spaces Banach space
# |* Z' h- M3 m4 [/ D8 E7 u# yBands Band (mathematics), Finite bands6 q8 ~- S3 G3 Z& `9 H W
Basic logic algebras- ?4 G$ K* k8 M. ?1 d
BCI-algebras BCI algebra: r( J# c) k2 s N$ p' }% V
BCK-algebras BCK algebra: K5 y; [: O# N7 g( J# r8 E1 {
BCK-join-semilattices
6 b, I1 {' h, a6 E+ Q" A+ FBCK-lattices
5 s8 p; U7 I0 `, X2 kBCK-meet-semilattices( ~ |! a! J+ g0 A3 N
Bilinear algebras
" g$ g4 g9 U) c; j: ZBL-algebras
p5 t4 B( U! H0 MBinars, Finite binars, with identity, with zero, with identity and zero,
2 q0 I: W' h8 V' u* n9 cBoolean algebras Boolean algebra (structure)
3 L8 J6 O! l0 L7 _- P/ dBoolean algebras with operators
. @- i- T' c4 jBoolean groups
/ s7 X0 L! ] E% yBoolean lattices
* k5 @! W2 l- U( H" @Boolean modules over a relation algebra* r/ o8 U4 h& P7 F$ W
Boolean monoids& G, i# {% q. P. P
Boolean rings: z2 c, O$ g+ g1 a: B! V5 \) E
Boolean semigroups
" c4 X: l- v& W2 B; `Boolean semilattices0 c. N8 a# b% a$ G5 W
Boolean spaces
3 R' A! S* m. O' w \! mBounded distributive lattices
# O; s0 A( O1 |Bounded lattices
, D4 X% ?8 }" E; \Bounded residuated lattices. D) N3 W m8 z! O
Brouwerian algebras
$ \# ^. h! {1 i) m/ n( |0 k4 wBrouwerian semilattices
( M( ?/ y0 e: b6 gC*-algebras. }7 m3 |3 ?/ {+ L W
Cancellative commutative monoids
# `" Q* o$ o/ Z9 E" O/ D7 HCancellative commutative semigroups
9 T, ?- [ Z* N% u9 i% h+ i4 }7 MCancellative monoids) n0 s: t5 \* E. ]' l
Cancellative semigroups
' ^3 X7 M7 L0 `' H1 iCancellative residuated lattices* C' @. i8 x; p9 q Q8 w$ i
Categories
9 d" o# |) Q6 m6 m( {# AChains# g* ]. f6 ]+ A* i# H- i! X
Clifford semigroups
1 I8 T" X# }2 V* {6 i2 hClifford algebras, F1 n$ Z! }2 G1 I. H9 Q8 L
Closure algebras# k6 ^" U3 `. J0 ?9 }4 `9 A& h
Commutative BCK-algebras2 W, n* G$ G: K3 }- c& [! _% P- N9 p
Commutative binars, Finite commutative binars, with identity, with zero, with identity and zero 0 H' o' q2 y0 V0 Z9 l
commutative integral ordered monoids, finite commutative integral ordered monoids, o8 Z2 d! u% I$ R9 v
Commutative inverse semigroups
( g' C" B5 ~% V9 o2 dCommutative lattice-ordered monoids; g+ }. v3 a ^" X% S1 X2 V( ^8 e
Commutative lattice-ordered rings9 i$ `" O6 y; U
Commutative lattice-ordered semigroups8 O& u1 ^% s4 p+ ]( W( U P& ` N
Commutative monoids, Finite commutative monoids, Finite commutative monoids with zero
/ p4 W6 F0 n" l7 QCommutative ordered monoids
9 ?8 A- q* ~" O6 @4 OCommutative ordered rings; P* ]& m- @6 w) k9 I
Commutative ordered semigroups, Finite commutative ordered semigroups
; B/ }; i" _5 H% BCommutative partially ordered monoids
, e M# s0 w7 @7 ~Commutative partially ordered semigroups
' }0 ?! K+ E! J! gCommutative regular rings
4 O- a" C8 F0 R. f& jCommutative residuated lattice-ordered semigroups
6 `" a+ P ~3 c1 U" GCommutative residuated lattices
' o: ^+ J0 b+ n9 S! |Commutative residuated partially ordered monoids M, T1 L/ d2 r# Y. w6 v+ F6 Z- e! S
Commutative residuated partially ordered semigroups
+ m4 l# n; Y& _8 P/ \ e& WCommutative rings5 B" x/ n& J0 P0 I V7 s$ {, A/ K
Commutative rings with identity
9 v* Q! ~8 l- I! }# q, _4 dCommutative semigroups, Finite commutative semigroups, with zero
/ B/ _* o) ?# P' LCompact topological spaces/ f! [# ^+ b/ u' ~+ p
Compact zero-dimensional Hausdorff spaces
( ?, r, I; a; h$ x& G" Y) nComplemented lattices" j4 t6 y" R3 s7 ~
Complemented distributive lattices" ~$ w* i) S$ w( h% o
Complemented modular lattices3 U& V* A( e6 B4 C7 v$ x6 }
Complete distributive lattices
# X( k* \2 N. B3 O' s# qComplete lattices
& W# B3 ~5 F% P0 H. eComplete semilattices& `$ m: _/ _- |5 P. @; w7 U. e
Complete partial orders
( w/ y+ n& |. c! R' i& ?6 @# j7 ICompletely regular Hausdorff spaces
1 V u/ o6 x# r4 q/ K2 mCompletely regular semigroups7 U3 [4 s% K' ~( K8 q
Continuous lattices% i4 V9 _4 O9 V2 X n
Continuous posets$ i/ W; z2 s8 U$ r% P* U0 @+ e
Cylindric algebras
9 K" {4 D" ` P$ g9 x% f9 n5 `/ ~De Morgan algebras7 D g' j v% v' d. N, {3 W
De Morgan monoids0 V( x+ w q( ~: H
Dedekind categories
' {6 ]; b/ s# k% e; KDedekind domains
- Q! W- j# p9 g- y# U. xDense linear orders$ w. _' s4 V/ M( L+ X9 q
Digraph algebras9 |& @ P7 J' w# G7 W( ^: z
Directed complete partial orders
I6 w# |, m! g- v. aDirected partial orders
; @$ {" l# S2 j/ q( _5 e/ m+ B' |) r" `Directed graphs
( b4 V/ g7 I0 c: M! ]Directoids
: a5 S6 L- }- s7 m0 c4 z4 CDistributive allegories
4 h0 ^* ?* a% CDistributive double p-algebras; C7 j. w* y# R! {" ?1 i
Distributive dual p-algebras
* ^, S. k1 ?8 _- n$ [( a2 k2 y+ l/ GDistributive lattice expansions. c* [1 K) M! p" s
Distributive lattices
, ?- o. }: v5 |Distributive lattices with operators7 w& `; C4 G3 A& j8 c( a( v0 E
Distributive lattice ordered semigroups
; d1 q; s' u3 _8 V! ~$ N1 R: pDistributive p-algebras: o0 p, h8 i L0 h
Distributive residuated lattices5 R4 a# r) E% o
Division algebras
5 Q! y9 u9 F# jDivision rings
+ L) {# q' E& I% yDouble Stone algebras
7 V8 `3 X i2 S q) }Dunn monoids0 y. N+ k2 U, w6 e6 u. Y
Dynamic algebras
' C: |& Y5 ~0 d1 CEntropic groupoids
% ^" _. D1 b' J2 [. ]Equivalence algebras) C w$ ]3 P4 C( R+ @" s0 a
Equivalence relations' a; ]! N4 B. J( U z% S9 A
Euclidean domains7 m4 e5 z" C+ B
f-rings) u, A5 h+ v7 ~. A9 Y/ R4 _3 |2 J
Fields, z" g$ z' B! ^# g
FL-algebras* f+ x" k* L2 {
FLc-algebras
% F5 Z8 f% c: w7 `. h+ ^/ u9 n. AFLe-algebras
5 t& E8 t8 ]# D: t1 ?7 lFLew-algebras
4 b( {' }% p ]/ n8 H# C* x. zFLw-algebras
: B3 i& z. l0 g& pFrames6 E2 u; T- A9 k1 W2 `
Function rings: f2 c& d/ j6 B; X. x/ k" q
G-sets) w7 w }* y0 X9 x$ ]0 |
Generalized BL-algebras
( m$ y( K& Z( D6 D6 `Generalized Boolean algebras
4 x: w- w* A/ J% [1 SGeneralized MV-algebras
" S" y# m4 U* z" I1 @& hGoedel algebras0 L! |: d5 G! X0 w% j
Graphs4 f8 ?) F3 @) g
Groupoids$ X- T, N( R8 ]8 C2 [5 e. w
Groups
7 [2 I( V; D1 tHausdorff spaces
7 q% K+ t, f' h0 i9 m- NHeyting algebras# s/ B* D+ f: x
Hilbert algebras
8 e, ?# L7 a8 A) |" T' [) u' hHilbert spaces9 N5 w* j% }' L f4 ?
Hoops% ]9 P1 `$ P) U' p5 Q0 W: n0 R5 c
Idempotent semirings. n* o2 w, S, X! g5 H+ z8 {! U+ @
Idempotent semirings with identity1 r) k% t* i/ \" i
Idempotent semirings with identity and zero
3 k U: q, S. T6 v. IIdempotent semirings with zero* w8 A' c9 Q0 q& C; I$ C- I
Implication algebras
) G6 D# E. D, d. B- O' @- cImplicative lattices' a% J5 `% Y, F* a# a
Integral domains/ T6 _6 s2 N0 F8 B) {
Integral ordered monoids, finite integral ordered monoids
' \5 P$ G% [' {Integral relation algebras
* I, ]1 P3 A) s6 uIntegral residuated lattices( O9 t' P& Z7 X" i
Intuitionistic linear logic algebras
1 e4 [4 o R2 ^2 U Y t& ^Inverse semigroups; o9 q: Q" G0 n# k1 W# n* c. I' F4 M
Involutive lattices6 g+ o5 T2 B# `( Z* Z0 O& A4 b5 Q
Involutive residuated lattices3 k( M7 o4 y) y% Y
Join-semidistributive lattices
" d1 ?0 A7 p+ @9 r5 VJoin-semilattices
+ {" ?8 g! ~- t1 u4 ^* A" Z- hJordan algebras: S& P) R: I3 ]$ r9 L; S; a+ C# \& N
Kleene algebras) ?' E$ I9 Y9 g
Kleene lattices
" D2 v& {, K+ d$ l4 ?+ ~ PLambek algebras9 N2 w0 S' q" _3 j% F
Lattice-ordered groups
% V l1 u- P f! M+ o. M+ vLattice-ordered monoids9 }, i, U& R% ?/ A& e
Lattice-ordered rings q9 ?; f) {! Q1 B4 k* O
Lattice-ordered semigroups: v# P: a8 S5 C$ O7 n# N
Lattices
/ r. q5 q. w" B* Q; A6 ILeft cancellative semigroups
2 E0 g1 [+ R( s; R: Y, ZLie algebras: b9 ]0 C, g- W- l: Y2 Y& ^
Linear Heyting algebras
9 v' |( l6 D; q6 e8 p* M5 \Linear logic algebras
' ]0 G6 V0 Q7 o$ r# P0 F8 ALinear orders
: A' r8 C9 H. k+ ~4 nLocales9 q# @9 Z2 q3 p1 F9 K# Y: D
Locally compact topological spaces, G" r: H) J7 s6 f) ]! \6 u
Loops
6 d$ ` G. P& U6 g. q# WLukasiewicz algebras of order n
c# g' I4 J- _M-sets) \5 Z4 U8 w* J8 r; h
Medial groupoids
7 c& h2 ~! ~4 o# [; vMedial quasigroups
+ Z. q0 ~& S6 ]# ~Meet-semidistributive lattices! B$ d9 N1 z4 p: g; _) Q
Meet-semilattices7 j$ d' O+ `1 j
Metric spaces6 H/ `2 d2 x2 `. @7 Y/ p
Modal algebras' @" Z$ P" n, P- `( u
Modular lattices) h% J/ _) J$ K7 L4 o! G
Modular ortholattices! A/ P9 x! j8 k7 w6 D: W
Modules over a ring8 C( }0 j9 |/ c& T4 J
Monadic algebras
- ? Q, {) k& Q9 u4 G4 _! P/ U) V# TMonoidal t-norm logic algebras8 ^% a, _0 {# B" r6 N
Monoids, Finite monoids, with zero+ d: h3 ^! x( G
Moufang loops
: ]3 l6 Q4 W9 i6 B. d* z. w: j NMoufang quasigroups
E0 K, C x) _; v/ B2 {/ XMultiplicative additive linear logic algebras
. N7 }' a, Z/ ^0 Q; {Multiplicative lattices' n( K" g" r1 f4 t
Multiplicative semilattices
9 z* _6 ?) z( h8 z( B: ~7 o- mMultisets
! U7 U! o: ?& B4 e% Z2 x4 N% f0 K8 RMV-algebras5 i0 h+ L* D n' q; y
Neardistributive lattices
, L1 y$ G2 K( r! `2 Z0 E: X% CNear-rings5 \' r7 A% A7 `# H9 `% r
Near-rings with identity
+ |9 Y1 x6 W; C+ J. ?Near-fields
9 T4 d5 h: {4 R4 m( E! t8 }Nilpotent groups8 U' e9 q9 F9 p$ h( y6 O, q
Nonassociative relation algebras) v+ ^* P; ~- @/ @9 o
Nonassociative algebras7 A! p7 @0 ]% x' K3 C
Normal bands( c& S7 p' M3 L, Q! w
Normal valued lattice-ordered groups" c/ H1 h7 b. v2 r6 J( }% E9 q
Normed vector spaces
* Y5 l) ~3 D$ iOckham algebras, \, r. [# S/ S$ E( I6 R
Order algebras2 T3 T* U, z& c/ R4 C( V
Ordered abelian groups+ B% p* C5 b; C( O" R$ _
Ordered fields
6 T/ {! B9 V# w9 f6 \1 }* qOrdered groups1 H* Y- s2 F: W" Z
Ordered monoids
. m/ U6 n4 V- gOrdered monoids with zero! a9 S3 E; y, | K6 F8 N
Ordered rings# G7 K9 F- O7 V, A# I* S
Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero
/ g" F% n) g' p8 R; U8 ~' _/ vOrdered semilattices, Finite ordered semilattices( W0 j3 o( l3 |( R; ~) W
Ordered sets
. ^8 Q5 y4 U6 _& F8 @3 J& g QOre domains [. q7 b/ L S5 W+ K; `8 H, P
Ortholattices, O- ~1 B1 m7 F, \( K6 [' u* |
Orthomodular lattices
4 c5 W/ y: K6 n. np-groups4 p/ O) R: N% V1 O
Partial groupoids6 ^3 R& q/ s9 _3 _; W `* G/ C) a
Partial semigroups
) {" }, Y2 d8 J \% B. FPartially ordered groups
" S" ]1 n6 B; A& ~) T6 k& HPartially ordered monoids: z- t* h5 J" Z& g# w1 l: p/ h7 Y
Partially ordered semigroups' X. G7 i! v& Y# v. z# N
Partially ordered sets
, t; T! {2 M$ Y/ vPeirce algebras5 k8 R, D- G1 U
Pocrims7 f# \+ T+ p6 W: h/ a" R
Pointed residuated lattices
! f, n( X9 M) P: c; |Polrims' B, n. U* m$ m' N6 C
Polyadic algebras
. X& w7 O5 ?' {1 D- W% S5 YPosets
' ^; i' n( l2 t! ~ h# j' wPost algebras
# M* D: m+ I1 W+ @- o9 LPreordered sets
/ O/ Q; P4 i& @% R" CPriestley spaces6 b/ h( t3 W# |
Principal Ideal Domains$ d# J- U2 ?2 V. t! a+ V% B, ~1 E
Process algebras ^( K* x7 Q9 \
Pseudo basic logic algebras
* [" @, a. O. s- y5 m3 LPseudo MTL-algebras
" {& K `; L% CPseudo MV-algebras; p& A3 K; h: a4 Q. A% n: ?
Pseudocomplemented distributive lattices
7 i+ C) S, ?% f- k2 `/ uPure discriminator algebras
9 r+ Y. t6 ?$ M% _' FQuantales
8 Y1 H; G9 N5 X4 x* O" m4 ^Quasigroups; m7 k" W- [" Q. {4 y. |* e6 \7 `
Quasi-implication algebras
( A5 D( i3 B& V% D8 yQuasi-MV-algebra
; J/ o; i/ L; V7 V& [$ Z l% L8 mQuasi-ordered sets, b7 f4 M$ F( L; z! l) K
Quasitrivial groupoids% w% L" ^8 @5 r3 B1 J3 B6 m
Rectangular bands0 E" k$ N$ f7 E. ]. e
Reflexive relations5 N: `) B8 [% H N. l: z5 J- T( v
Regular rings+ x4 R. r0 O2 _0 c0 F" ] y! j# D' l
Regular semigroups4 r& l& L$ \5 G% _* f4 `5 `) E
Relation algebras5 X/ ~& O: g8 p$ D
Relative Stone algebras
3 d( g. S E. i, i5 G! mRelativized relation algebras2 N: O, w% i! p0 h& D. N: f
Representable cylindric algebras
# t0 G/ A( F3 G# e* KRepresentable lattice-ordered groups
D6 D8 J; z- `2 Q* vRepresentable relation algebras
( y& i5 w2 }! ?: cRepresentable residuated lattices
$ _" A G* B( C( i4 }Residuated idempotent semirings# `5 R0 Q6 P* K1 C) [% D; }/ j8 e
Residuated lattice-ordered semigroups
2 X( _2 t' @, X1 XResiduated lattices
% J. @* V% s8 y4 O' r2 ?" hResiduated partially ordered monoids
0 |: e: P1 F: }# N4 dResiduated partially ordered semigroups8 l& H& V+ E$ o( ~+ a
Rings
6 @- _- s( _9 I) {) b' X7 bRings with identity, Q( P/ H. C1 p4 h6 g
Schroeder categories: k7 t) B0 r+ n% ?8 _
Semiassociative relation algebras) r, _" C J0 M
Semidistributive lattices2 k8 H; O: d2 T n: u
Semigroups, Finite semigroups2 I, n: D) E! J6 i
Semigroups with identity( H% ^& g6 K W" [6 s: k1 u
Semigroups with zero, Finite semigroups with zero
! l' P! {! i: ]$ S9 LSemilattices, Finite semilattices
; ~5 s: F9 a. A8 E2 R& ~6 ]1 ESemilattices with identity, Finite semilattices with identity% B R4 @5 N* R9 {+ @
Semilattices with zero
. }# M$ |- G' a0 w6 X! r# JSemirings
5 N7 a A( d% \. DSemirings with identity
- j- e0 v: v8 G$ zSemirings with identity and zero
( q b1 {7 e% q0 V {1 ]Semirings with zero
2 o0 M8 ]0 s' U/ lSequential algebras
6 t* v- T" f3 Q1 R: z9 ]) rSets/ ~) A7 z' G s! q: G' M% |
Shells
, N4 w! E1 D7 W' @9 y" }Skew-fields, n2 f5 h6 _" s. \6 A$ p. f
Skew_lattices. a5 C+ @6 `# D4 t* }% L* O7 S" v# F
Small categories
8 d, u0 P2 G; }" LSober T0-spaces
8 t) ^4 L W% p' s: R/ JSolvable groups
6 ?2 ?0 o; m. ~9 \Sqrt-quasi-MV-algebras! C4 t4 e- H% D/ V) t- b0 ]
Stably compact spaces
% u0 Q. H! I' ]1 \Steiner quasigroups
1 v7 A- C" Q3 y- Q1 J$ W2 NStone algebras
% Q K6 L6 U8 w% U! e+ t+ P) q' XSymmetric relations
! W) `' P9 O8 M! T5 _T0-spaces
4 o! B6 @ t3 |! H) ?6 q7 aT1-spaces5 U$ L( i9 | _$ l0 Z( |2 I6 j* D
T2-spaces5 x& ~2 q/ i7 r" I/ z( q1 o
Tarski algebras: |9 d! S1 K, ^. Q
Tense algebras
1 _- j5 x2 r" ^' kTemporal algebras
# W. m( Q% x$ L! m! r+ MTopological groups* a! U/ D1 j) a7 S; c2 m7 Q) b
Topological spaces
9 K: h. `/ w7 C4 @( W `Topological vector spaces$ e5 [$ {. O9 j H* h* q! L
Torsion groups$ r3 z3 E; J( U
Totally ordered abelian groups& i" V3 [. T1 f
Totally ordered groups
; ?& ^/ P% B2 V* J p4 @Totally ordered monoids+ Z3 e, C4 K" e8 Q
Transitive relations3 ^7 ~. o: p3 i' F7 k
Trees
" y# `+ j4 ^. s4 X; J2 O1 M! @Tournaments+ Y2 g4 y9 i9 D. s. u6 [
Unary algebras% j X/ z; i. L
Unique factorization domains
}, P0 X3 T1 _8 f4 B" S. FUnital rings7 ]. w6 u$ N8 X$ g: h6 _( U
Vector spaces- ]/ y* A" C& E3 z7 B% s2 z
Wajsberg algebras
. w& J; c/ j. c' h! ]. T6 b- n3 O' MWajsberg hoops
7 A6 q5 P5 p1 ]8 p! ~* qWeakly associative lattices
3 `! \9 c: T: G# a7 i6 S+ M( P# eWeakly associative relation algebras
- ` I$ t, q3 G [; gWeakly representable relation algebras9 N/ p: M& e& P0 c8 m+ u6 Z
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