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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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8 [* N. c: T5 `, L! l: b; D& o
8 w: g, _) }; X" {; z: v0 z% b4 H/ ?- MAbelian groups Abelian group
5 r8 T- S D4 \& N$ @- ^8 Q* WAbelian lattice-ordered groups
. v0 K9 P& D0 u" y) P |2 `) c3 g% nAbelian ordered groups- G. w* T' r+ e5 R8 E3 c$ }
Abelian p-groups
- z. |) J, ]* T" {. SAbelian partially ordered groups
( g9 V8 L3 v& i+ W/ m& |Action algebras Action algebra5 D, @8 @- C0 ~4 l5 H: d
Action lattices
# q" d1 J- e* e4 D+ KAlgebraic lattices+ J: _. H9 N& U* I
Algebraic posets Algebraic poset
# x1 N; z2 @( z/ W: x# NAlgebraic semilattices
% t% W1 S4 J% [9 M; T! G0 _Allegories Allegory (category theory)+ f1 A, F( P9 Q; k4 e$ Z. E
Almost distributive lattices; E, T, p: @1 a* f7 f. C# i
Associative algebras Associative algebra( |, s* B4 f# S H0 z! X
Banach spaces Banach space
/ {0 k/ B9 r( FBands Band (mathematics), Finite bands
3 ]9 C' r1 E9 Z7 Z2 DBasic logic algebras4 J$ [3 W/ m- B1 y3 h
BCI-algebras BCI algebra2 I/ Z( D- l9 h
BCK-algebras BCK algebra4 T3 F/ k& i/ w4 B# ^- R0 s
BCK-join-semilattices
. @$ [# U- H4 LBCK-lattices7 E5 J0 f. t$ J+ A- @
BCK-meet-semilattices
+ R' H+ Z( M1 N/ C! WBilinear algebras+ @9 x& p6 R' l: d- [
BL-algebras, B. y C* E8 q$ a7 P% ]
Binars, Finite binars, with identity, with zero, with identity and zero,
* g$ t( h0 M( E* }5 k+ H. J- `5 L" mBoolean algebras Boolean algebra (structure)
9 i: N& C/ {6 ]% v6 b1 M# l: ?' TBoolean algebras with operators
& }7 i: M0 ~+ _/ k( X* v' hBoolean groups
) O' ~7 x* C5 R; x3 y7 w4 ?5 ~Boolean lattices7 j8 o8 s/ p& Y1 M2 h
Boolean modules over a relation algebra' O% x- Z/ H/ h! ^2 D
Boolean monoids
& Z* t. s; n; U/ y; O; |Boolean rings
# r# F" ?. w! f3 Z0 r5 CBoolean semigroups
0 G% K, I; T6 _ [) q. vBoolean semilattices
8 u0 c$ z" _, IBoolean spaces
6 _/ A( P ^, Q7 Z8 ^; ^8 T4 \- YBounded distributive lattices) T$ y# d6 J9 j! i+ I4 E
Bounded lattices
, S1 c, d/ s1 FBounded residuated lattices
. \0 ^8 \$ W. B# F5 eBrouwerian algebras4 q6 r1 A( T% q& h$ z4 c% y
Brouwerian semilattices
$ g0 _. X2 z+ }& zC*-algebras
7 J/ U1 N6 y3 l1 M& [8 {6 SCancellative commutative monoids% B* _8 X& I6 q* c3 l, z+ W
Cancellative commutative semigroups
' ]/ Q9 ^* D! D# rCancellative monoids% Q4 K% {* Z0 Q+ ]+ f; ?
Cancellative semigroups
0 k- `2 c8 ~5 Q3 |/ w& VCancellative residuated lattices
, i1 a6 x/ I) ]( t; LCategories' e, o6 b7 t+ O$ g
Chains
; @4 s& Z2 R/ c: zClifford semigroups
/ p; q3 M/ Z& FClifford algebras
; J& Z2 V2 w6 N7 \5 rClosure algebras
: r3 P9 ?$ v9 \+ _( _Commutative BCK-algebras
. ^) @" }( l# T- n% b6 pCommutative binars, Finite commutative binars, with identity, with zero, with identity and zero 2 Q/ [ s1 t, }$ e; u5 r& K! G
commutative integral ordered monoids, finite commutative integral ordered monoids
0 X3 V/ l' f, KCommutative inverse semigroups
$ P% F* E6 A: c9 r4 `Commutative lattice-ordered monoids1 M- B7 a/ }/ ]4 D! K; M
Commutative lattice-ordered rings
. X7 l( c) T, Z( x8 z% u3 WCommutative lattice-ordered semigroups
1 b: ]& ?- t% Y! G xCommutative monoids, Finite commutative monoids, Finite commutative monoids with zero
E9 K# _: v; C/ m( @, GCommutative ordered monoids* X0 J9 ^' |, {/ Q a- J. i0 s8 K
Commutative ordered rings7 d$ e1 s5 I4 D0 v B- j
Commutative ordered semigroups, Finite commutative ordered semigroups
/ `$ m4 |' S* fCommutative partially ordered monoids
/ J. @3 J s X- V' o3 K& wCommutative partially ordered semigroups8 E6 @) ]1 U/ Z5 i. M
Commutative regular rings8 S6 d$ w+ I+ R, {
Commutative residuated lattice-ordered semigroups
6 @6 _2 q! f# [! S$ S% I1 sCommutative residuated lattices
7 n! @! ], R" A& V& qCommutative residuated partially ordered monoids4 _# N+ J1 ` i7 L! G- ?+ l
Commutative residuated partially ordered semigroups
$ a3 I. X$ n0 d" sCommutative rings
$ ^, H$ M* y! S7 i& @0 tCommutative rings with identity
9 b' B. f' w; Z' lCommutative semigroups, Finite commutative semigroups, with zero9 V9 f& t: L. x. Y |9 F
Compact topological spaces* ^, a4 \4 A# K# R( }' M
Compact zero-dimensional Hausdorff spaces2 p4 [9 c! p: }. K
Complemented lattices. b0 t% `/ G( i
Complemented distributive lattices. h! G# p. p z5 Y4 ]2 i
Complemented modular lattices
' a; Y7 H- e" N) a8 CComplete distributive lattices, N2 T5 F5 l: q3 [
Complete lattices
$ X" ~1 B4 T- s1 M- V, UComplete semilattices# S: S: |2 V4 U; }: f$ n" y
Complete partial orders
1 d* Z8 N# v6 ?3 \1 C4 n$ UCompletely regular Hausdorff spaces
( N) @$ ?& Z- \1 I& M }3 ?Completely regular semigroups: r0 Y1 l% V7 l3 s! K& P
Continuous lattices
- t1 Y: x$ z& z+ iContinuous posets# O4 O( E( k+ @# w7 _
Cylindric algebras& S' l% U+ v2 D/ z8 c- L! W$ `
De Morgan algebras
6 A; W6 b. o! n9 t, B+ ?& L" V( ]De Morgan monoids5 O# u* v' X0 S( H+ ~- [, X9 d7 }7 J
Dedekind categories
1 A9 z* C, a _" iDedekind domains
z) S9 T+ L+ ~; S$ }" mDense linear orders
, R5 f( g' \' e9 ODigraph algebras+ d2 y9 D: _& s$ n2 x2 w* L4 g
Directed complete partial orders v- f" j7 z, G/ D( u0 a
Directed partial orders0 d, p" _# H* y3 b2 K
Directed graphs
+ _. C* G% d, o% N" e- c5 [Directoids
( }& D8 d( ]1 d. {9 x* D& hDistributive allegories0 E2 O* |& [4 O
Distributive double p-algebras R; q7 K: Q+ K, w
Distributive dual p-algebras" o* c, p' G/ n7 F( M
Distributive lattice expansions: W" C3 B# n6 r1 P5 E& N* L# N
Distributive lattices8 e# c( n3 {7 T/ U6 t9 C" U; T
Distributive lattices with operators
9 |; V4 A8 {& K6 w& k2 DDistributive lattice ordered semigroups
* K% O; l$ V/ ~) ~Distributive p-algebras7 ?0 B& e* Q: M) @. u
Distributive residuated lattices
! j' w+ X& o. G4 }' |8 }7 i; |Division algebras5 L4 d& H0 ^# l0 x! I
Division rings
8 w5 V1 t: v% QDouble Stone algebras x* r9 W4 p' e. h: V2 v
Dunn monoids
' `) G1 ?0 u# B8 V- H, nDynamic algebras
7 r. M# l1 K) |4 ?1 K, WEntropic groupoids
* E3 j8 ~7 t- V" w1 HEquivalence algebras) n {5 E Y0 T4 u6 |
Equivalence relations
5 V* R& u- j% s; L _8 M; ?6 _Euclidean domains( s4 p4 }- r! Y M$ k+ e h; |/ k
f-rings N$ k+ @5 F' H# j7 i8 h# K% O
Fields
' f! t1 _" C- I3 B! W" IFL-algebras
u" H; L/ x$ FFLc-algebras
& a* v5 Y ?' {) W' _' XFLe-algebras
3 N3 _7 N5 U! F8 S4 i/ ]" Q7 F1 WFLew-algebras/ i) {4 a; O0 P9 `7 \
FLw-algebras* N3 g* o- D, V8 \" S( T
Frames7 e) r \7 Z8 t- z! Y0 K5 H5 V [
Function rings2 a z0 A5 S5 y. K* ~$ W' D& `
G-sets
. R( I4 @! w7 j7 V; \0 D0 LGeneralized BL-algebras
9 K. N3 I0 o8 SGeneralized Boolean algebras
* X5 u1 f4 `9 u. E8 BGeneralized MV-algebras7 W9 s& L5 Z% q# B" M# H
Goedel algebras) B! x8 }; Z/ z5 c. |, l3 M
Graphs, z9 E q9 V6 @" x% P) g5 x5 I- K
Groupoids% s7 K) n0 |( b0 M$ n
Groups
% o( m. E" _8 n% P' JHausdorff spaces
0 j- o- i2 A1 b. C; ` e HHeyting algebras* Q- g5 ?2 W A- y! E: j
Hilbert algebras3 R9 s( o d) ` T7 J
Hilbert spaces0 Y7 y1 A; d F {8 ~
Hoops/ z7 P N$ V. t4 D5 U
Idempotent semirings
& ^+ j# p! W# c9 \+ IIdempotent semirings with identity, @ d2 z3 s7 Z; j J0 o0 y3 l
Idempotent semirings with identity and zero! A# q; O8 T# D# p- e
Idempotent semirings with zero
+ L- |2 j1 L6 Y% i1 ?, d* M6 iImplication algebras
4 j# O$ C5 { f: p$ fImplicative lattices
* z% U* Y4 u3 c$ H8 P% x8 i- hIntegral domains) Q- f$ }6 u! ~: b( j* @. @
Integral ordered monoids, finite integral ordered monoids( D& j# n0 j, y/ d
Integral relation algebras) p/ W/ p* z A2 f+ v7 [* D9 e1 v
Integral residuated lattices9 P, Q: C" o# M: Q# n
Intuitionistic linear logic algebras
% c8 d# d' E! c% g# |+ h/ ~Inverse semigroups" r) R, d1 _% U( S4 [5 I _
Involutive lattices
( g0 }+ m; |, n, JInvolutive residuated lattices
( R9 m4 M+ h+ E' d7 YJoin-semidistributive lattices) M, b N9 E; F
Join-semilattices, ^# I# c& C* Q. _0 c. `0 c5 r* }
Jordan algebras t$ x# U% k+ ?- v0 d, P# h
Kleene algebras& V3 t/ r, I, w! E* z$ \ g
Kleene lattices6 G9 q- j6 K3 j
Lambek algebras
3 x4 o- [) X: {! ULattice-ordered groups
9 y6 o8 X1 ~; a( f) O. Q( c% GLattice-ordered monoids
2 n- Y' _) v" Q+ Q8 A$ VLattice-ordered rings
0 R; X2 U1 m; d( LLattice-ordered semigroups- ^0 R4 d; z/ c1 y9 S8 f2 z
Lattices' X6 O+ q( u6 s, }0 V+ Y6 u
Left cancellative semigroups2 x' {/ u$ [" u1 A( e
Lie algebras
3 J& w( \+ A' y; z3 {' aLinear Heyting algebras& ]1 F ?0 ?7 u" P3 Q
Linear logic algebras
* s/ j' `% N# M( u; P* B# H) VLinear orders/ J. w- n0 B9 x' k! ~
Locales9 x7 m' P! y! {
Locally compact topological spaces
, z) K" z* |+ I% hLoops7 ?) L, j) H4 R- L( `2 f1 k
Lukasiewicz algebras of order n
5 R/ I0 L' s7 t3 `& k' GM-sets/ e, n* n$ l! O! V% O$ t G0 D
Medial groupoids( `$ S: V/ c9 c# h3 ]- X4 T
Medial quasigroups4 z, V" O! f! E" q8 v
Meet-semidistributive lattices6 C% j9 W, ]# V9 t) j r
Meet-semilattices
" m; S2 U. m E2 aMetric spaces
$ R; J. S5 Z2 S; ~3 VModal algebras, a" P; S! T8 ^4 z
Modular lattices5 N) i7 _, c4 ~9 q3 @3 m3 J
Modular ortholattices
/ W& p: @* \5 I! P" }+ mModules over a ring
) G. S! l' u6 i Q, f" N4 a. \8 T7 nMonadic algebras8 K; M' \% x' X3 T
Monoidal t-norm logic algebras e; f* s1 a c$ H
Monoids, Finite monoids, with zero+ i9 b, H1 |7 E" @' c
Moufang loops$ [; }+ T6 W( k* d+ n$ @5 b
Moufang quasigroups
" A( b) N3 o6 W1 J" j9 p& y% BMultiplicative additive linear logic algebras/ A2 z* H0 ?* h3 q) i! N8 Q% D
Multiplicative lattices6 |6 K8 O- r U& A H! F$ F
Multiplicative semilattices3 }. A/ L8 ]' X- [
Multisets' L; j& Z9 O1 o5 g- x5 Q
MV-algebras
' @$ S A8 Z; D7 y* N4 tNeardistributive lattices. W0 y) b6 z4 e; ?1 L7 K
Near-rings
7 ~) u1 ?7 L. e, |- P! D2 v+ W5 SNear-rings with identity6 o- I/ X# M$ L' d l
Near-fields. ^0 N& S9 @6 G7 T
Nilpotent groups
8 P, l6 j2 }, G* K6 T9 s$ O _Nonassociative relation algebras
( {1 K! {/ x5 p+ \3 @Nonassociative algebras$ S% t+ S) ^! v7 j* z' K
Normal bands
$ x) m9 [0 q. `4 S+ YNormal valued lattice-ordered groups% w" |7 u- t. s0 d, B. v2 [
Normed vector spaces
. g- ^# ]: G& V# g5 P2 ~Ockham algebras5 t7 E2 V) Z( z
Order algebras0 \5 C8 E5 A* Y [
Ordered abelian groups3 u, `4 `' a2 E( y6 ?2 k
Ordered fields/ G, f2 J6 D' r* J' c
Ordered groups2 }. \4 |6 ]7 `3 T) {6 B
Ordered monoids
8 }) j- v. U; ~, U' a; FOrdered monoids with zero- n* w! b* V h7 q a+ L+ l
Ordered rings
9 o" ]# _2 \9 S2 F" ~# g! gOrdered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero6 Y2 t; c! d. G$ ]
Ordered semilattices, Finite ordered semilattices
% I1 W$ [* K8 [/ B0 KOrdered sets
: g& `/ ~/ R) i* W+ OOre domains
% c) \, B9 {# ^Ortholattices
' G3 l/ _ j* y5 b1 ~' I. bOrthomodular lattices' Z) h( F$ F: W- r+ X
p-groups0 C7 ?9 A" ]( y Q) }, S- P9 N
Partial groupoids
$ p1 T0 h8 o+ n6 r" G5 }Partial semigroups+ i9 N+ @) s+ D" Z
Partially ordered groups
, ~, W& L5 _+ i" k" V' y& nPartially ordered monoids
4 P9 u2 Q/ B; q1 APartially ordered semigroups
. ^$ M/ N$ X" S3 e4 q, RPartially ordered sets% E. p" }" p; L8 `1 `
Peirce algebras
9 Z) S8 ]( h6 APocrims
7 U5 l# p/ X2 V- q Y2 h lPointed residuated lattices
- G, m; K; b9 r) J4 f3 r" x* u$ w. {Polrims+ @ W" K) D9 o2 P2 C
Polyadic algebras& ]3 ]( q, o3 y, G2 { x+ I
Posets8 X6 C" p+ \! i/ v0 x7 D. a
Post algebras# \* E$ r# }' O8 z+ x: L& \
Preordered sets8 B- h3 d( [* L, T3 X/ `( ?. Y) y
Priestley spaces+ M' |4 O* Q' J' N% c2 F
Principal Ideal Domains
: q, y- A$ Z) r% D& tProcess algebras* F" ?! Q9 t# T9 m1 @0 J
Pseudo basic logic algebras
) U- a, h8 H! M( i: f4 |Pseudo MTL-algebras$ ~& i* h: N$ p" t, d% L2 i
Pseudo MV-algebras! V7 U. B8 k! t: v J% B5 G
Pseudocomplemented distributive lattices0 P9 w% C8 i+ e3 O
Pure discriminator algebras
" \. [& P/ g, K" z; C+ k+ [( nQuantales
4 s3 d# e8 r! s1 [0 Y8 g" OQuasigroups
: b/ I, y5 `$ ~$ M( nQuasi-implication algebras# Q* y7 w2 b( B9 c) M5 D" f
Quasi-MV-algebra
4 R& A: ]# ?5 q- m0 WQuasi-ordered sets
' x! B& e! \/ T1 w$ GQuasitrivial groupoids
8 q8 ~, ^, X" e. B7 z6 }Rectangular bands( W; z0 \: J0 J- x+ U$ ]6 a& l
Reflexive relations
% w6 M% H+ o0 S. LRegular rings
- K O7 m( z9 \% h9 D6 \$ z5 wRegular semigroups: t1 d9 l/ I' u% |$ U4 e
Relation algebras: O! T$ W+ L& I9 x
Relative Stone algebras
, }% B4 C& _) W: ]& @9 ?; ?Relativized relation algebras) @% p1 ~ }1 e5 t/ L% f- a2 c4 m
Representable cylindric algebras7 a1 A& h% N- d( W
Representable lattice-ordered groups0 ]3 ]1 u. e- W4 I6 x( u
Representable relation algebras
6 ?9 e1 N+ q* p' s7 |6 NRepresentable residuated lattices: L3 R. `, A3 U! y9 }) \/ X
Residuated idempotent semirings
! i5 n: v4 @* ?! t8 |2 z1 F- l: sResiduated lattice-ordered semigroups
) d+ y& M6 g& y$ c! h) b9 m b+ ^. EResiduated lattices
$ d- k. J. j* pResiduated partially ordered monoids7 {+ |5 U7 R; d9 Y2 W* l5 \# T
Residuated partially ordered semigroups
1 J2 Q7 ]9 N4 \ Y* rRings* e9 a# }, Z/ `6 {( y; K- \% B' P
Rings with identity
5 O& y4 O7 q6 y( D% XSchroeder categories
9 |! W0 v% T( n/ P$ b/ cSemiassociative relation algebras- t9 L3 {( |6 w2 V) @8 ?1 n: W
Semidistributive lattices+ ]5 @' j9 i. q5 e
Semigroups, Finite semigroups
' C# I9 \5 W6 B/ ISemigroups with identity3 n) V+ I5 p9 E- [5 a1 d. l
Semigroups with zero, Finite semigroups with zero
& ~* O6 B' {% XSemilattices, Finite semilattices
7 U7 F- x4 }5 `' b9 \8 a$ L S+ ZSemilattices with identity, Finite semilattices with identity
2 F# _4 k$ s! a3 ~. [% \Semilattices with zero) q0 g2 F' A+ H: e8 c8 W6 `$ }/ ^
Semirings
; N6 v- j0 M0 f1 k; E5 wSemirings with identity) x+ e7 D1 n$ }4 H; Q- k+ w' D* d
Semirings with identity and zero
0 S3 z# u1 Q; f# v8 NSemirings with zero8 F, C/ U$ c; {
Sequential algebras! B. E9 ^( q* A i5 j! a& t# X
Sets, H' a; n0 ^6 K1 ?9 W9 m
Shells, X: j6 P! g* N7 L
Skew-fields+ S S2 {( g& x7 |5 Q* {3 s0 r- X
Skew_lattices
: K' M( b; e5 H1 C- u/ E0 E" e4 jSmall categories
7 `: j8 e" T# t* n/ [$ e. h; LSober T0-spaces
8 m7 f* R5 u1 B7 GSolvable groups. q* c7 ^' N9 F1 C( G: p2 ^
Sqrt-quasi-MV-algebras
/ i4 V, c9 O! O* kStably compact spaces
& y! x/ C* F" A. GSteiner quasigroups. U$ S5 W4 i2 `8 q
Stone algebras
2 P% o" B+ |( n7 q9 tSymmetric relations
& Y& X' ?9 r) j+ g: {T0-spaces
B. D# Z2 ]4 W7 {; _8 x) r( ?T1-spaces" |5 v& W$ O9 F0 n' X/ Q
T2-spaces
; }: ? N) Z0 b5 b1 p: |Tarski algebras
6 B3 J1 w2 g4 m+ UTense algebras2 R: B6 J8 s$ D
Temporal algebras; P+ `( j+ o% V- a: e
Topological groups0 e" A L* {7 d% X" I
Topological spaces# z" |" j, o& |: G7 v0 g
Topological vector spaces. A, |. S0 @' a2 a
Torsion groups
* R$ r" N; i+ vTotally ordered abelian groups
! M y+ N* \% k, l& n- BTotally ordered groups0 [2 i0 l% [6 `" A& w1 w
Totally ordered monoids( g$ K. @! k0 B
Transitive relations
2 P+ m3 V6 |) A6 v) FTrees
* R" ~+ h& z9 h: E. kTournaments
3 W# C! O' G% t! o6 RUnary algebras; }) y1 D& S5 ~, Q" m8 `, u7 T
Unique factorization domains
' n* n( p7 A! `3 X* P9 ~4 B: n6 xUnital rings
' r; ?1 z& e% i( XVector spaces2 j! T) i" @2 e# a
Wajsberg algebras0 w l2 b; X @7 q
Wajsberg hoops k7 ]/ A+ H1 R5 G8 B8 s6 ?
Weakly associative lattices
+ W& P, u w9 Q" e7 F }Weakly associative relation algebras
5 {/ _3 L4 m+ k9 \ o. KWeakly representable relation algebras; b* u& s2 E& {# ^$ V3 U
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