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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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! f1 p: T7 R1 @5 j* [
; i; @' [7 C: FAbelian groups Abelian group* y3 }* F7 C* u2 ?
Abelian lattice-ordered groups1 y* [' {, T! ?) C0 W
Abelian ordered groups2 f' }8 ?: y5 `* ^
Abelian p-groups# T2 G' f6 o# l5 h; A9 z
Abelian partially ordered groups
' [7 T2 ~( q- A0 oAction algebras Action algebra. w7 ^5 b L* B, a$ x' v
Action lattices- h& |7 o$ \5 A
Algebraic lattices1 q5 L7 X( {0 I& C5 ?5 R
Algebraic posets Algebraic poset
% L3 e+ w" D7 O- Y( pAlgebraic semilattices$ [: j$ u9 I' d K
Allegories Allegory (category theory)
( S+ J: T' y9 o( E5 F+ Y( n5 pAlmost distributive lattices
' \& w* K- k/ ~+ WAssociative algebras Associative algebra
( ^+ y \$ t0 e9 qBanach spaces Banach space
" ?8 }$ [& E6 p" P, L5 k4 |Bands Band (mathematics), Finite bands
- D# _/ |3 y# A# X! d- fBasic logic algebras
4 R1 Y/ y7 |, ^BCI-algebras BCI algebra8 L ^5 j* Z% R/ L) z! c& m
BCK-algebras BCK algebra- G. F- |& y, r0 \
BCK-join-semilattices4 S% F% S8 o; v+ R% |& ^& h' T
BCK-lattices
5 D+ i5 ]( d: kBCK-meet-semilattices) S5 Y) s- w2 y% Y2 ?6 c n$ K
Bilinear algebras
# L! Z- v* q, o: F- sBL-algebras: c: U! E& F* i5 _, k
Binars, Finite binars, with identity, with zero, with identity and zero,
, A4 a4 U; ^# Y, \ P* h( GBoolean algebras Boolean algebra (structure)
' G0 g3 p8 r5 {2 W E' vBoolean algebras with operators
, R& a9 b5 h9 F0 [, [$ W8 F CBoolean groups h! M- E( V+ S, _
Boolean lattices5 f1 S: P" ? G
Boolean modules over a relation algebra$ {% L3 Z/ ~, s2 ^+ S
Boolean monoids7 A$ L. M' `, I) G" U3 Y, g
Boolean rings
6 Q. o6 E3 J& J% J/ o EBoolean semigroups
. j0 I. ^5 ~* N' [" XBoolean semilattices( L% Y2 O. M: U- G" _" D
Boolean spaces' q9 {$ R) X8 E( M n& [* F6 C3 f4 b
Bounded distributive lattices. ^$ m2 \! ]7 @" y" L; x2 o8 P
Bounded lattices
4 M; J& A- C) O6 z: V8 bBounded residuated lattices) N2 h" I; v- K1 z, @0 m
Brouwerian algebras
# _8 e' R* P# x$ q- O0 ABrouwerian semilattices
/ @. p: O$ k1 U8 q, G1 B5 ~C*-algebras
0 Y S4 {; E$ m$ w% ~- P7 w( |* _Cancellative commutative monoids5 p7 X" w4 f4 Q
Cancellative commutative semigroups
) y% R" C, \: \6 m: E: l4 W6 oCancellative monoids8 _; W4 q9 Y" X9 w) n
Cancellative semigroups4 w9 |$ z2 U0 G6 z* g1 A) ^" i- `
Cancellative residuated lattices
4 _- Y4 F. ]9 U1 x* NCategories8 P/ l1 ?- @. a$ E! X0 V
Chains- J' `$ E2 K5 Z: s
Clifford semigroups
: x4 X5 W* K. U9 yClifford algebras; J* L% M4 c/ c1 e/ [
Closure algebras
" e4 u5 Z: Q3 |! ^1 xCommutative BCK-algebras1 ~" X* x1 n; F" D- K
Commutative binars, Finite commutative binars, with identity, with zero, with identity and zero + V+ l' J2 b1 I' X, { b
commutative integral ordered monoids, finite commutative integral ordered monoids
2 _& d0 l* E0 g; p+ F& }Commutative inverse semigroups/ X! a6 {% B9 K3 L
Commutative lattice-ordered monoids6 m) o! t% k X5 l, ~! R
Commutative lattice-ordered rings7 X" w! V3 H" K! ~& I" z5 `
Commutative lattice-ordered semigroups
% A, B; Q, z5 o7 CCommutative monoids, Finite commutative monoids, Finite commutative monoids with zero
9 b* z* F4 }% I3 pCommutative ordered monoids
8 j+ \5 r/ ?( T7 p3 [0 \$ CCommutative ordered rings
9 ?4 x$ f6 ]% x" V4 i$ ]Commutative ordered semigroups, Finite commutative ordered semigroups: _( w2 A! l# n' C. U" l0 X
Commutative partially ordered monoids
. m0 J8 F: C6 J: w: xCommutative partially ordered semigroups
' z K5 o: s1 T! TCommutative regular rings f, h* w( f. X( k
Commutative residuated lattice-ordered semigroups! v$ Z O; A- f* |) E/ H* o x, M
Commutative residuated lattices
4 d3 {! h. {) n9 y- E iCommutative residuated partially ordered monoids
0 i+ k" r2 E/ S5 K8 q; j3 BCommutative residuated partially ordered semigroups
2 J0 n# X& @* Y( z4 [Commutative rings1 {+ u: x. s. D( c3 j
Commutative rings with identity
& w3 [& T: [3 Y, L" I) P/ @Commutative semigroups, Finite commutative semigroups, with zero
& e/ U* m9 z& _: u* H5 d0 c6 wCompact topological spaces
1 R: _. ?( {0 \: [' b8 cCompact zero-dimensional Hausdorff spaces9 g% |9 q' D6 D' f, B
Complemented lattices
( J4 ~" k* {6 ?8 Y3 f4 ^. kComplemented distributive lattices+ U9 C6 F7 T) T4 q
Complemented modular lattices4 D J+ T; K' P& A' ~
Complete distributive lattices
% ]0 X# F) ?% V) BComplete lattices
- a3 }* X& P; u7 g9 M: O- A# G0 x' cComplete semilattices, o! R/ f A8 d a3 N) Q" B
Complete partial orders
8 k2 T* B" W4 T# qCompletely regular Hausdorff spaces9 n# M# W+ q& H h
Completely regular semigroups U6 z, x5 _* i) m& d% y) m
Continuous lattices
$ T; U( D/ S& ~& jContinuous posets
+ o& c C$ s! ?, W, UCylindric algebras
7 l2 e# a& c$ D' tDe Morgan algebras
* w/ c, w {0 d d3 L1 Z) `De Morgan monoids8 U. f: A% s8 U/ ~. u" R
Dedekind categories
$ r4 r0 m1 p% X- ^4 rDedekind domains
7 ?6 U2 y- O+ w$ e2 W+ @Dense linear orders
) U, W; Z$ d5 g) t' D; ODigraph algebras4 w0 z! U+ U4 r, S
Directed complete partial orders
7 b5 c' f! h% _# R# U7 g: kDirected partial orders
' m$ p# p; w3 p e: uDirected graphs9 N* O' A2 P `8 j+ Q
Directoids
& I/ e; T) c) k. a+ @: NDistributive allegories8 y, w! Z }+ S K7 ?$ P( G, y
Distributive double p-algebras
, O8 _4 Z8 z" bDistributive dual p-algebras5 ^$ T0 [' g6 a Y" T5 |
Distributive lattice expansions
. m! }1 \) E, K ` WDistributive lattices2 Q( v# Q8 _, }. r+ H! t5 q
Distributive lattices with operators
2 h2 ~2 ^) v6 m3 v6 M) r1 q! y7 lDistributive lattice ordered semigroups* A6 R& P0 K5 s u8 Q9 f( B
Distributive p-algebras3 r( | ~% i% |' }
Distributive residuated lattices7 Q0 V- j. A2 n$ ]
Division algebras
9 D0 F8 M; H" ], x# M0 }Division rings( q2 a1 K9 L- j4 e/ j
Double Stone algebras
$ o" m# i" K& \3 RDunn monoids
7 b! u9 j4 ?. i0 m8 \ k- lDynamic algebras6 |* h$ g3 u+ p0 I' k b* w4 Y6 C9 z
Entropic groupoids
- O( V, R$ L. U, P+ O/ c# o4 hEquivalence algebras( g( O7 u9 n5 R( X$ N7 ` Z
Equivalence relations) y8 _8 b$ Y% a' h, U
Euclidean domains9 z7 C$ j4 z; p( u v0 q
f-rings
5 P$ f, j3 _6 w lFields
& M4 O3 H! v: F! @3 r/ l' Q1 CFL-algebras5 ^; E6 ~8 K* k+ z/ u) @& I
FLc-algebras
: u* F5 t# w# a" H% `) P: B( W" wFLe-algebras
) [& t7 x5 e. o d8 qFLew-algebras- a u+ u7 Z* J
FLw-algebras( {& I: t1 j" |5 `- U
Frames
9 Z- h) \1 X- Y9 k9 S+ AFunction rings( Q) {! ?. ~; S2 A" r5 r( d: Q
G-sets
) N# r" a6 l r" y% @/ pGeneralized BL-algebras" U, J3 ]- g- `( U9 H. j1 J' w9 O
Generalized Boolean algebras. q1 y; }' u8 q! p
Generalized MV-algebras
" ~4 L* ]+ T; ?8 D" I9 F eGoedel algebras
; v# s. k- c5 [1 AGraphs
% X `+ l" m. U4 u1 K0 MGroupoids8 O3 w9 [. Q8 W. i
Groups5 [' N- v9 e$ B6 A
Hausdorff spaces) e4 r$ m4 Y: P& [
Heyting algebras. E) I/ }9 V- ]5 N$ d
Hilbert algebras
6 ]# k' f5 v8 b6 E8 qHilbert spaces
$ k- U8 `9 j& T$ |, x! m7 jHoops3 t' K/ ]9 y0 {& x8 c7 D
Idempotent semirings$ m" _( C. H/ q7 \/ M- Z, @! ~
Idempotent semirings with identity9 Y+ L) F" I( L2 o A
Idempotent semirings with identity and zero
! R9 L4 D8 s! ?! H2 n- c2 _Idempotent semirings with zero
- e3 i* A3 {2 ^, \/ Z* `Implication algebras- \- `7 Q2 p! D/ m+ P$ X7 ^
Implicative lattices9 i) t! K; i3 k' \5 {9 w+ Y
Integral domains5 f. V0 Z* o, H" _6 y1 E4 L" L
Integral ordered monoids, finite integral ordered monoids
! y$ N0 v: R( i& rIntegral relation algebras
, m; O9 H) I$ n/ x4 u3 QIntegral residuated lattices
0 _1 w/ ~" p) lIntuitionistic linear logic algebras0 v2 I- C' Q0 m3 N: Y a
Inverse semigroups5 q+ i' N* _! R6 I S
Involutive lattices
8 W3 k! }$ m( s; cInvolutive residuated lattices
8 d. S$ M v7 qJoin-semidistributive lattices6 [% r: ]9 e. [2 P! A9 i8 W
Join-semilattices6 n9 M! V% C% f3 }' O- k
Jordan algebras
* ~) A$ Q$ Y# Q' MKleene algebras
& D" Y5 I, g Z/ \( ?: b7 B4 P/ NKleene lattices
% V1 X1 h3 M0 N) p' @, ^0 K6 a% [Lambek algebras3 [7 T2 ]# ?* o) P4 O% n- Q$ a
Lattice-ordered groups
2 k( C W' h$ ~9 H6 s! [Lattice-ordered monoids
3 a, k3 D0 H& f# l2 p6 |+ nLattice-ordered rings
, T# s4 l0 \8 _Lattice-ordered semigroups# T5 {1 Q4 d& c3 {
Lattices9 E0 O! v2 S5 L: M% n
Left cancellative semigroups
! d1 W0 A5 d8 Y, ELie algebras6 R' {- y O) ^$ g v- | E9 e' @
Linear Heyting algebras) z2 P% j: Z! M
Linear logic algebras* l& y% r8 I8 l0 g
Linear orders+ l7 w5 E- i6 a" _4 Q
Locales
. q; ^* D" l1 ^! I p6 K: ZLocally compact topological spaces g3 N5 A9 a* p# B7 p
Loops
1 Y/ F: p! R7 E, H% u# R+ QLukasiewicz algebras of order n
9 \) ^5 O# y4 C$ P# aM-sets4 v1 R+ Y. n5 V9 ?2 N8 B8 u; v. d
Medial groupoids# P: A5 }, U% b: y; [
Medial quasigroups1 F# I: o+ p& b3 g* [* l
Meet-semidistributive lattices
+ R3 U" k5 U6 P! tMeet-semilattices1 s. x3 v* f! [4 x' {
Metric spaces( {4 m3 t4 b. p2 P# v, I6 \2 B& k
Modal algebras2 |9 _$ a5 P. U& ]( h# d
Modular lattices: P. Y6 Y1 g. }. ^. a4 i: Y
Modular ortholattices
. i, {8 t3 w" T" _5 ]5 c8 ^9 @Modules over a ring4 M; Y% C/ i S' G$ S% h$ P# |2 ?% ?" e
Monadic algebras1 y, \8 ?, R! X" e, f! G* C% N
Monoidal t-norm logic algebras+ N) m( S- t$ T3 w. d0 I5 R9 A
Monoids, Finite monoids, with zero
m, A2 z% B% g' p+ R; fMoufang loops# |8 E% x/ |/ o: b+ @( M
Moufang quasigroups& b" E# O3 ^9 ?8 i7 p& y) t: g3 U
Multiplicative additive linear logic algebras2 B2 [( R7 q3 N
Multiplicative lattices
* @- q0 e/ h4 p f' R: ]$ k" j% |Multiplicative semilattices+ B* j d$ H# w2 A4 V% }7 r
Multisets
- k7 w4 |' | A% LMV-algebras
2 w6 G, H* R9 v7 d6 uNeardistributive lattices
% Y. _7 G+ O7 @: j6 A4 }# ]. CNear-rings
( P) V1 E3 Z9 x3 o) n* @ L |1 M, |Near-rings with identity
4 Z+ J2 V( I0 y/ @4 }Near-fields
$ x3 j6 _/ [0 \3 q, t8 Y& @Nilpotent groups
. v, V3 g* a7 T2 G3 N( ZNonassociative relation algebras, K6 {0 ]2 J0 G
Nonassociative algebras
; |7 u: R. Z) m. l, R% S CNormal bands
& q3 \7 J2 x2 GNormal valued lattice-ordered groups
0 Q9 t% V O5 zNormed vector spaces
3 ^; [9 S5 n( K* E4 |Ockham algebras1 n3 W# N2 Z9 ^5 Z( g
Order algebras2 p6 _) s/ n& p/ x0 v% t6 b- X
Ordered abelian groups
* J8 z$ @* a% l) Z" g7 K. ]Ordered fields
, f3 n+ b0 s3 w( m6 E' GOrdered groups
$ Y& F( p) _$ ]8 Z1 }& n QOrdered monoids7 a# M5 E7 R3 }1 I6 @0 H
Ordered monoids with zero0 b; |* F6 B, I# M. Y
Ordered rings
4 m( @" l2 t3 }Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero* ]# S' f& V, }
Ordered semilattices, Finite ordered semilattices( z8 w8 Y N' P8 X$ C
Ordered sets
8 P2 P% D/ `( G9 }, u% EOre domains1 b5 S2 w. q5 V1 ?% m; t: ]
Ortholattices
( P! G+ F. [! K" G* r- w2 C# r" LOrthomodular lattices
, z5 ?; h! r, m5 t( wp-groups
) B& I4 k% t/ H+ ~3 jPartial groupoids
& ~, o% R) ]# s FPartial semigroups
1 Y. [$ K( T3 APartially ordered groups
3 K# n* H8 B# {. kPartially ordered monoids% J, x9 f) A4 j. I8 Y
Partially ordered semigroups
+ U+ r" M4 Q6 `5 A8 W# JPartially ordered sets
" z, n9 S g4 e4 U# Y6 F9 H! JPeirce algebras
/ k" {9 H4 R$ [, A/ E( pPocrims) |! c+ [: K) z5 v
Pointed residuated lattices: g5 f: U; D* H) ?0 P0 [
Polrims* T4 E, H/ v" K2 ?" y
Polyadic algebras' e2 Z( q) r2 N# i
Posets$ G+ F- V3 E: y& [* h. @
Post algebras
( \4 O; x' \5 x2 K* ~$ ?$ hPreordered sets
( b( w& H2 u1 O6 WPriestley spaces$ c- H* [$ l' `4 C, i
Principal Ideal Domains
, g1 b9 d8 d0 |' z' \ SProcess algebras
l: k' [: d( g8 x2 zPseudo basic logic algebras
1 a8 g0 x% [7 ]! f# W6 _/ j( yPseudo MTL-algebras- u8 m) E5 f- B" ?+ F$ w
Pseudo MV-algebras- X6 _' ^" q( V% B K3 {- ?7 q
Pseudocomplemented distributive lattices) q6 K# d4 S4 B% T- }$ n, P
Pure discriminator algebras
7 N5 p. X9 c9 I- ZQuantales5 H' _* F/ ^* e+ d$ h1 X
Quasigroups! A" G( r) G7 F( L; W
Quasi-implication algebras
8 X/ E4 D1 [# E6 d% |Quasi-MV-algebra7 { b. f5 r6 [( t
Quasi-ordered sets# v% m0 l2 S5 ]5 H0 M: |% M
Quasitrivial groupoids; a8 ^5 U5 T* B+ p/ d# V: x; m0 g0 r
Rectangular bands* ]& ?- `) ~' {
Reflexive relations9 p' X, O6 r- E5 ~$ p5 a1 q
Regular rings0 \6 P/ z+ ?5 ~, g
Regular semigroups+ B4 a$ X; [) g
Relation algebras3 ?+ w! K: A/ Z8 e6 q( m# w
Relative Stone algebras* ^/ K2 K6 R# i, y
Relativized relation algebras
, d7 h p4 [& ^/ A' R* v$ x, nRepresentable cylindric algebras3 Z; h! ?, v1 j' I3 y7 C
Representable lattice-ordered groups0 P& F4 x6 {; p" i$ q
Representable relation algebras
9 F- A2 ^9 s0 f& R7 b# v# hRepresentable residuated lattices2 y. c7 ]% r( J. i0 T6 U* o+ P" k
Residuated idempotent semirings
& x0 @' a; m2 Y9 U: H2 {0 U+ r" SResiduated lattice-ordered semigroups* d! ?+ c& b9 h: i X- J6 X
Residuated lattices2 O1 G- x, A! r
Residuated partially ordered monoids7 N/ o$ {; R/ Z
Residuated partially ordered semigroups
1 Z2 L( V1 k% Y6 a* R6 o+ ^/ VRings; u3 [5 C1 F8 ?$ F. K: S
Rings with identity; Z1 q0 U8 {: {* s
Schroeder categories) g* p1 e4 B5 s
Semiassociative relation algebras
- }# Y3 `+ J _# xSemidistributive lattices/ ]) k9 \7 J* ?; a" V: s! [4 P1 R
Semigroups, Finite semigroups {# e- L- Z! P4 u
Semigroups with identity
. h+ b8 z# g+ V% ?Semigroups with zero, Finite semigroups with zero' g% @) I3 e; z# l# {$ n
Semilattices, Finite semilattices+ e# h4 c; d* M% Z; ^& D
Semilattices with identity, Finite semilattices with identity7 C0 c$ E! U7 [' o5 Z$ J
Semilattices with zero) D& X$ h( d" r" A/ ?
Semirings
9 W+ D, j! e+ V( f" g: qSemirings with identity1 N+ a1 G* |1 U1 Q% N# }0 S# t
Semirings with identity and zero5 E; N# _" j" a" F# ]1 Y! X s n
Semirings with zero
! Y j) e# K( h8 h3 @Sequential algebras% k; {0 [2 q4 h9 T( c5 K
Sets7 V* |8 L% L3 F: B# t7 R
Shells
( o4 o! l3 P! g3 S" ~% m5 DSkew-fields5 r. e: m2 H% K8 B
Skew_lattices2 }7 P6 ` e3 U6 K3 ]* \
Small categories |# [0 m% q( H) x; Y
Sober T0-spaces* I; M4 W, F, I) Y' C7 i; V3 x
Solvable groups
1 V# s1 M) V( b# b! qSqrt-quasi-MV-algebras \! h$ X8 L! H: m+ o
Stably compact spaces
6 Y$ j' M. B; v/ h! Z8 U2 bSteiner quasigroups
: [. B. S8 P* U' k1 e" mStone algebras
. Y4 A7 t* _3 w( ?5 O2 OSymmetric relations! D& E- L5 M" J- M4 @# |& O" v
T0-spaces0 r% k3 z+ g+ i ]: Y6 f
T1-spaces+ J- \; h/ c0 z, p# Q& ~0 \% ^1 }
T2-spaces1 z. U E: M7 y; x9 l6 ~4 _
Tarski algebras2 o1 |: F$ D0 M4 E& L z7 r
Tense algebras3 c4 O7 k- Q& U t
Temporal algebras2 @% g3 B; [# z. J2 p
Topological groups! f/ @4 U6 |3 }1 {/ u: R4 O
Topological spaces K. B5 Q, w- Z+ a, j
Topological vector spaces) U: i4 j; ~0 z2 h1 O3 O
Torsion groups% K# _% U- f# x6 o9 L4 T( T
Totally ordered abelian groups% U; P* d4 d4 [6 h/ T
Totally ordered groups
2 B1 e( K& |7 ?# k W& W2 w4 FTotally ordered monoids! {5 j8 _, L( X) i* k; C
Transitive relations/ `, r/ n1 H- Q( G' v
Trees" {5 @0 m/ w/ [/ I9 e
Tournaments
6 a7 ~. _6 l Z, g0 Q6 _. e5 GUnary algebras
" [, k4 [; |3 C9 ^7 P9 fUnique factorization domains( ^7 {9 ^+ u, b( Y
Unital rings
+ [* \6 X3 m5 _2 n4 n8 aVector spaces
! U I M6 h0 D# V4 dWajsberg algebras0 c0 d9 k" C* n" n4 ]! m
Wajsberg hoops
# Z/ P; {& ?* ?% HWeakly associative lattices
+ |' v* K3 t( IWeakly associative relation algebras4 S* d( q- K% R; q& i
Weakly representable relation algebras1 ^1 V. p( O0 D9 x* b. ~6 ~
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