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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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; C( q7 K# Z) n4 y' C, l# W
" B! x& u: W+ X# lAbelian groups Abelian group
1 ]. {9 j4 I! P7 @; k+ t" C' @$ u$ uAbelian lattice-ordered groups3 N! f# |0 P$ M o# E: r# p
Abelian ordered groups
2 S) ~! }3 a2 {Abelian p-groups" H- v% ^2 i# E, ]; V( t* m
Abelian partially ordered groups
8 d6 r( q0 `9 o! J; ?$ XAction algebras Action algebra7 M: R( M& ]( B% i. L! M: u# p8 J
Action lattices7 d' u1 Y) m; g
Algebraic lattices
! w- |$ _ |% u% I4 O. yAlgebraic posets Algebraic poset
1 @5 Y, p2 G8 e2 jAlgebraic semilattices' v: r& v1 M2 c8 Z
Allegories Allegory (category theory)
: d: }4 n. Q+ [; t0 ?Almost distributive lattices& p! H% |" l8 w, l
Associative algebras Associative algebra! ]- F7 l+ C, I, K; @( f
Banach spaces Banach space/ [9 F( r4 J- L2 {+ U A a5 }
Bands Band (mathematics), Finite bands
- f) L$ X' R& X: GBasic logic algebras$ ]5 M' k/ e! { @, d1 l
BCI-algebras BCI algebra
8 f; L! G6 p$ HBCK-algebras BCK algebra
7 E" b* F- @! Z# R9 W- F: U7 s% }1 yBCK-join-semilattices, N# U c% y1 k. s' Y* q
BCK-lattices3 s1 v/ v- v; K+ c; N
BCK-meet-semilattices5 I, @& R1 V: w2 \, i& v0 W
Bilinear algebras2 B% O" p8 `/ R0 N7 T
BL-algebras4 j* E* b: u/ F* T% ^$ M6 ~0 U& Z
Binars, Finite binars, with identity, with zero, with identity and zero, - }3 a( R; V# V# I4 n
Boolean algebras Boolean algebra (structure)
: ?( T/ v2 m" D& K4 |Boolean algebras with operators/ } F" h' C! d
Boolean groups! i* f, ^8 t/ ~4 c+ @
Boolean lattices- t$ a4 r$ x8 [1 d2 r# w$ `- V
Boolean modules over a relation algebra% a* @& ?9 z" P) \8 N- e
Boolean monoids8 }" @' I, w V+ W Q3 L8 r
Boolean rings: E+ U' ? @. T$ q
Boolean semigroups
8 i5 G6 N! B, {. \: s3 D7 \Boolean semilattices: l) _7 |2 {4 F2 [9 a' j) I
Boolean spaces+ {% Y$ [8 p) n
Bounded distributive lattices
0 ^$ R. C' Z8 Z c4 u" zBounded lattices
8 C* U! N2 _5 N1 {Bounded residuated lattices
( Q4 j6 y8 q2 {: ]5 p7 tBrouwerian algebras+ P) {. Q% q5 S, W
Brouwerian semilattices
8 k& C( W9 l) e$ n0 h' X1 IC*-algebras! m) p$ K% _4 m
Cancellative commutative monoids8 c2 a0 U+ I1 n' N2 v% s
Cancellative commutative semigroups- ]$ E- b4 ~, K2 @
Cancellative monoids
8 n3 L3 _( M. ^5 _! |- W# nCancellative semigroups8 \% Z! J5 z4 N0 I( E
Cancellative residuated lattices0 t9 X: a2 k3 b/ }- Y; i
Categories
: a8 ~+ j! W- p w. X5 RChains
2 m3 [$ {/ e% z5 A6 uClifford semigroups( N9 V& h* B* Y8 h, G1 ~( |0 X
Clifford algebras+ |7 y; N0 ]( R( J4 d& G
Closure algebras9 y! p# G9 g B; o( B/ c6 T
Commutative BCK-algebras
9 j) A; V. b, [ M4 {2 n% [Commutative binars, Finite commutative binars, with identity, with zero, with identity and zero ; A% H5 s9 U; d1 S% I1 ^5 V# Z
commutative integral ordered monoids, finite commutative integral ordered monoids
7 n0 \8 L4 Y7 L D z/ {8 S+ LCommutative inverse semigroups
- i# Q3 e+ I' s) pCommutative lattice-ordered monoids
: u$ r4 I8 J( X9 jCommutative lattice-ordered rings9 Z7 Q7 y0 h1 R
Commutative lattice-ordered semigroups% V, E% v! H1 u
Commutative monoids, Finite commutative monoids, Finite commutative monoids with zero: N! o1 j+ n* N$ |( T
Commutative ordered monoids
/ }2 o0 P. X4 CCommutative ordered rings2 Z& _' [4 `* ?
Commutative ordered semigroups, Finite commutative ordered semigroups; p3 B3 @% F/ C$ o* `+ z- f
Commutative partially ordered monoids
( X/ c" D9 b: y( I$ f) LCommutative partially ordered semigroups0 Y5 ^, @9 a0 s9 E) F' {8 A3 o% W
Commutative regular rings
9 W# r9 e4 x9 W- O% CCommutative residuated lattice-ordered semigroups* U4 m6 [7 q) F9 d
Commutative residuated lattices
' @8 x/ G. ]. o# ~Commutative residuated partially ordered monoids8 q8 V9 q; h! ~: R R
Commutative residuated partially ordered semigroups
6 ?3 s2 P. f: ~% l, t7 e7 }" ]Commutative rings& g. C5 Z/ x# b8 g6 R
Commutative rings with identity1 ]3 Q7 L7 |0 [5 N
Commutative semigroups, Finite commutative semigroups, with zero
: s/ x) H& a$ L) r) F: TCompact topological spaces
( m$ h: w4 ~" n* x0 ]9 LCompact zero-dimensional Hausdorff spaces( p+ i$ y: m4 Y3 V$ g# l
Complemented lattices
5 H5 m* r- i9 ?% ~8 VComplemented distributive lattices7 U m* Z p, m' W
Complemented modular lattices
/ v& `# _, s: E0 e7 Q8 O, QComplete distributive lattices7 l$ Q! ^/ G- v: h) I
Complete lattices! f" f7 A9 |- |1 Y5 g7 Q& l
Complete semilattices* I* Q8 M; ^7 x, j; F1 m1 \
Complete partial orders
& \% G1 }5 O; t$ t8 Z1 W# SCompletely regular Hausdorff spaces
& z, H; g( f- u6 O& R+ f% h3 _1 ], _% QCompletely regular semigroups% s$ j+ |9 y. @3 L7 j/ d
Continuous lattices
: m8 x2 w! f% y( C& z8 P0 aContinuous posets( c/ N" r [0 G8 }3 j0 J9 d
Cylindric algebras( Z; O/ j1 F! a4 S; ^3 W
De Morgan algebras
, k( b' M2 N1 J, S' j# T* FDe Morgan monoids7 S) P$ w1 Y, e0 D3 q
Dedekind categories- u0 o4 n4 d9 r6 l: ? C
Dedekind domains& O, A" E4 N) @5 H* Q) p/ H$ k; S5 H3 Y
Dense linear orders- G% U5 A# L* A6 g: l" E/ W4 ]
Digraph algebras
1 n& j2 S) E, pDirected complete partial orders
! W, l$ e+ Y; _8 }6 N3 U0 v4 ]( _Directed partial orders
* _; H4 s3 l2 _% X' d. }8 O0 |Directed graphs
+ ~$ t# m a% E: L* lDirectoids
& T0 U9 a" h; }1 a" p) YDistributive allegories+ f5 M1 h: W# f" w) r3 z4 l7 Z7 U4 V
Distributive double p-algebras# q; p3 d1 W' U; w# C2 z
Distributive dual p-algebras9 Q/ k: U7 e6 _1 c, v! f; G5 P
Distributive lattice expansions9 Y) B; c8 O% r3 }9 y6 C
Distributive lattices8 A$ p8 P5 O6 ]1 c) x) p. j
Distributive lattices with operators0 Y: Q0 o: `( Q3 n8 v' O% o
Distributive lattice ordered semigroups
" y8 o& i7 T- k/ X, Z! h2 ODistributive p-algebras
5 M) C; A1 Q3 {( o4 WDistributive residuated lattices
4 q, c- E8 }0 F5 n* j" m9 eDivision algebras
' D: S3 g& t9 c3 t3 m6 ~' XDivision rings
: q+ W8 L6 _+ _. c& D3 d' e9 sDouble Stone algebras9 [3 E( l* Y! S4 k' y- R- l( j
Dunn monoids
3 x7 Z/ O! W* NDynamic algebras9 h; ^* `* [( M
Entropic groupoids' T4 p/ K6 L( _5 x5 v0 z
Equivalence algebras
: x* ]" G% z# D6 D# U. BEquivalence relations
5 m/ b' T, j- e! D- z$ W$ h9 IEuclidean domains
. I4 J% K* m! f0 sf-rings3 l. M$ W; n2 u, ^6 L5 F8 Y
Fields
, p9 t U8 S) s. AFL-algebras
, V. P! ?5 p1 I4 {) B: IFLc-algebras4 @3 t4 z' n+ b
FLe-algebras9 Q5 {4 B: H2 A# t- N1 ?
FLew-algebras
" |# T( K$ r- R5 Y6 |FLw-algebras9 l7 U+ s: g8 q7 ]
Frames
# c% h! e7 {) D( vFunction rings
2 ^( j8 O# Y) `6 eG-sets( L8 A4 c! m% l) B- }& F( z, \5 _3 M
Generalized BL-algebras
7 [. b$ z. i3 }Generalized Boolean algebras
: e3 g2 }/ P5 X3 qGeneralized MV-algebras
: c# q# Q3 S1 v! p) JGoedel algebras
$ {0 W/ }) q: S8 ]- l6 `2 J' ^2 T) qGraphs1 E1 w( O# I" l a4 U% b
Groupoids
, z& P) r3 k( ?Groups) W! l' R/ R2 b1 l9 M' ^; x" E
Hausdorff spaces" g7 D1 d8 x V( J: e3 f
Heyting algebras n& S4 L: X! |) p
Hilbert algebras7 P3 u$ e# H! E, O1 s' w
Hilbert spaces
4 d8 b" z& m. D9 AHoops$ Q/ H. [( _+ w- t
Idempotent semirings
0 o# \' m F3 F1 E+ ]& d1 y6 KIdempotent semirings with identity
5 j6 l+ ~6 o, B9 UIdempotent semirings with identity and zero# ^# Y X7 O$ W: \
Idempotent semirings with zero
4 {: q# x0 p( }/ XImplication algebras
0 _0 Y; D/ y6 ?& `* l6 {Implicative lattices
0 D, | P) i$ `; LIntegral domains2 |7 \' t8 N! b) ?2 Q! X
Integral ordered monoids, finite integral ordered monoids
' }6 Q3 z2 ?' a7 z5 NIntegral relation algebras/ t; @9 X; L, ^+ M, S
Integral residuated lattices* i, Q+ y- u$ C5 I
Intuitionistic linear logic algebras9 F1 [+ r( I; c/ O+ ~
Inverse semigroups
* a4 ?3 v5 s G' j# F2 tInvolutive lattices$ Z6 ]6 o P* R" `7 }
Involutive residuated lattices% f( x( P0 X6 M; C
Join-semidistributive lattices
3 x% t3 b n$ {Join-semilattices+ q7 j3 j( @, t6 n* N, Y7 {3 B
Jordan algebras! ?9 S5 l$ m" k! e
Kleene algebras
2 ~/ D& [# r' o' S1 ?2 IKleene lattices7 z* Y7 v( p2 Q+ |$ o! ~# ]
Lambek algebras
5 O I7 x0 G, L! [0 K' zLattice-ordered groups5 [9 ^: w# q3 P
Lattice-ordered monoids
4 A8 @6 ^. q" l& W+ pLattice-ordered rings ?! r) n: a4 f% ?) h
Lattice-ordered semigroups* f& W. L7 z, r# S8 E
Lattices
. I: s" g3 U. S! X: B6 q* |* [3 jLeft cancellative semigroups
4 X% r6 M2 u3 A KLie algebras
. g. D/ _7 Y% f* tLinear Heyting algebras; `; E; B4 Z; P
Linear logic algebras& O1 l h7 s' e! Y0 K
Linear orders
0 J) I3 v; E9 e+ s+ y% yLocales
) w: x- Z" |# O' a' i0 ^Locally compact topological spaces1 [8 m) E- y! D* b' d
Loops
* k/ A7 F8 D) n" }. y# zLukasiewicz algebras of order n+ p* J+ n7 P$ C1 U, e4 l
M-sets
/ b2 e0 @9 l* y7 xMedial groupoids" m" G A. m) x) F0 O# g/ w
Medial quasigroups
$ B- v8 K3 D) ?Meet-semidistributive lattices
' c& ~% e, G/ O8 F: } yMeet-semilattices. ^5 C+ S0 V4 }; T) X0 W
Metric spaces
: F( T+ }% {" e/ N; i, ~! Y% ?2 w# aModal algebras- Q8 n9 w+ j# t
Modular lattices7 l' `$ T k9 {' \' a+ f1 Y" m
Modular ortholattices R R4 }" Q# e Q i, C; z9 n( B
Modules over a ring
5 d* \4 Y- Y8 U& KMonadic algebras' l" F) E& l% b* K0 ~
Monoidal t-norm logic algebras9 v7 Q1 N! v( y2 S B5 q' i& O
Monoids, Finite monoids, with zero, q2 Y) X; t6 P5 i, I, q
Moufang loops. `6 z( _3 @. V
Moufang quasigroups
. Y3 z& @! O5 M: p6 f& o5 g" QMultiplicative additive linear logic algebras
1 H7 C& |) U' r( x; V6 uMultiplicative lattices
/ T6 r. G% U/ S& t4 AMultiplicative semilattices
/ G$ z' o4 v3 J( L1 SMultisets
. k5 t# u( y' n0 P P: x/ CMV-algebras. q# V+ f( G* D0 z, _, K
Neardistributive lattices
* p$ ^- v) i7 F8 ?; M0 ANear-rings/ Q$ J* P( C/ i, [5 M* |0 v- D
Near-rings with identity# j6 Y/ U0 Y) q1 |
Near-fields
1 [2 f# `2 e, @Nilpotent groups
4 s2 u# b0 f& v1 j6 MNonassociative relation algebras
! s9 w% H; N6 V! z0 Z+ RNonassociative algebras
$ b2 [& M8 @5 S: Q7 SNormal bands
8 ]+ p6 i, Q& r% zNormal valued lattice-ordered groups- N, r7 X5 J2 x& ?6 `
Normed vector spaces
& F# F* d% \+ m$ U# J1 DOckham algebras
# l5 ^+ T8 c$ {2 o1 BOrder algebras
_1 I& c/ J M+ E. j# H& AOrdered abelian groups8 Q4 [1 P$ @9 R
Ordered fields
- c& G7 x9 n+ i( K+ t' A% QOrdered groups
+ y: G7 W4 m8 k+ TOrdered monoids
/ ]5 o& ^; {. ]6 |# w: X% K8 gOrdered monoids with zero
9 P! W$ M$ h6 @( u9 oOrdered rings' z: |( J2 A+ K- M) H5 ?
Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero
8 ^6 X$ Q$ K- @Ordered semilattices, Finite ordered semilattices6 E8 S0 j6 a+ z0 O8 O
Ordered sets
5 q$ O/ D; r( v0 U6 _Ore domains
1 { h ~1 C, ~8 [Ortholattices) `+ }2 u l+ P7 Z
Orthomodular lattices
, J4 s- \4 y) C+ n! m; ]9 ~# Mp-groups+ r0 D' ]# P& l" l* q$ r1 J/ q
Partial groupoids' v) @- T7 }2 T" E# g
Partial semigroups; a2 x( x4 y0 d7 \# Q- T. |7 ]% @8 {
Partially ordered groups' d6 j& ?4 Y6 s4 r- m3 M8 U5 v
Partially ordered monoids
U8 D: Y1 r' T. n, H& `1 o9 TPartially ordered semigroups
$ G# R3 ~7 N9 H( V* zPartially ordered sets6 q. p7 l4 D3 p+ f8 Q- W
Peirce algebras
7 a. ~" r+ H+ K0 a; l2 K! nPocrims- k e7 [2 B# g8 E7 l4 ^- X) \
Pointed residuated lattices) n3 E7 \8 z8 x3 s- W
Polrims
4 L' {, u, w `, }Polyadic algebras
" a B i3 I% ^) H3 j L9 ~' }$ UPosets
+ Y" Z8 `% q8 z0 _* C+ L: Q8 J3 aPost algebras
- z# q$ \ K) f8 GPreordered sets
/ N, v4 _) O7 K3 P" dPriestley spaces
! J+ m7 _, [1 S2 N* EPrincipal Ideal Domains/ B1 z" d" T+ w% j+ r; X
Process algebras( m+ O2 h9 A6 G1 u5 w
Pseudo basic logic algebras' f e1 o# t7 P: T( _4 g" e4 h. G) `
Pseudo MTL-algebras) G) v4 X1 ?3 m6 l
Pseudo MV-algebras
4 V6 o, }3 v! @Pseudocomplemented distributive lattices
- V8 B0 x0 G- r& |0 o* ?Pure discriminator algebras3 T7 B1 ~. k1 U F* r% Z
Quantales; g! r/ N, X& J D3 y* @6 g
Quasigroups
$ f9 U! G5 c; Z, |Quasi-implication algebras5 h6 B2 k2 v& v6 u. d( `
Quasi-MV-algebra
4 C! Y0 H" Y! F- X w$ ?Quasi-ordered sets9 Z( b. s' m; E2 X# Y
Quasitrivial groupoids+ P3 t, w( t/ X3 P7 U4 |8 p! y
Rectangular bands
7 x9 ?6 `( q5 X0 G' t' X2 }* gReflexive relations2 x% h1 m3 E7 C
Regular rings
6 r; g- F* A' ?! L4 u) ~, TRegular semigroups
3 z ^) l7 J( j6 U$ _3 x i1 ?# D# iRelation algebras
; A" Q+ Z0 @0 u6 ERelative Stone algebras
1 V7 `5 C" W0 x) tRelativized relation algebras
. P( j0 p5 y3 TRepresentable cylindric algebras
( P" E4 d5 o6 q( y9 MRepresentable lattice-ordered groups
) _$ [0 ~. S# O( J9 z+ NRepresentable relation algebras; `1 g, K" D. ]+ W) S( C
Representable residuated lattices
8 ~0 S$ v, d8 v" K: T# B: o" `6 ZResiduated idempotent semirings
) {2 k' a7 l' EResiduated lattice-ordered semigroups2 L& V5 X3 t( Y. E+ a' s
Residuated lattices, d, N& o9 k4 y; ?- j' @' P
Residuated partially ordered monoids3 M. D& R: J% n0 u4 J+ j
Residuated partially ordered semigroups! W+ a2 @7 d- X4 i. D3 X6 w
Rings; e! w; P9 b5 O J
Rings with identity
3 ~4 u- M; @, C7 USchroeder categories! m( i/ |. C# a7 J4 ^
Semiassociative relation algebras
, u/ L. o* |* n; r5 OSemidistributive lattices$ m# W; l* g* \1 m
Semigroups, Finite semigroups
' f. U4 {/ E8 {% E2 |9 \: NSemigroups with identity
' U$ v' U& u. t' [7 qSemigroups with zero, Finite semigroups with zero; O+ U' B5 u5 h
Semilattices, Finite semilattices! B7 y. K( n# X$ }# M' ]9 V! W( T Q
Semilattices with identity, Finite semilattices with identity
' C1 w* v0 x* z$ s' y! OSemilattices with zero
" l5 ?/ o+ h% W0 e1 w$ L U# x: tSemirings
7 [0 X1 ]7 o6 G4 d# ~/ w8 E! G- oSemirings with identity/ t+ d& w: X0 G4 y+ r/ Y3 x# T
Semirings with identity and zero
# [ d/ B; u+ `4 [7 E: y7 |Semirings with zero# R& E) V* N( s; g- L* i4 C4 o
Sequential algebras; `& t. b; T4 ]
Sets
2 n9 b: {% ]. p. ~3 |Shells( i" Z! O ~" \, M
Skew-fields; I2 e- {; s5 ?
Skew_lattices$ r7 z+ k: ?2 u3 @- R( R
Small categories
* }: X- C5 r2 n7 o3 d0 ^* o/ d3 y4 ySober T0-spaces
5 o+ ]- v' k8 z, d% t+ W7 NSolvable groups
; u6 t# D3 ], J) F" n% zSqrt-quasi-MV-algebras0 f% k8 W2 `& |( Z" Y
Stably compact spaces' F& g6 a) ]; j3 x9 X! c
Steiner quasigroups2 ? |) x# Y; o6 ~- H( j8 E
Stone algebras1 ~, O; I2 \9 I, t
Symmetric relations& c5 {& j1 B. n$ X/ P
T0-spaces' X9 L) d% X" I; ^3 r
T1-spaces
$ f$ w# _3 p) p. f: m1 `8 ET2-spaces4 [+ E) k4 W+ `. {# G. x! g7 b
Tarski algebras
0 E3 Q# x P% i4 j! O l+ b& tTense algebras9 l' t: i+ i9 _5 U. U* z; ^9 K; n
Temporal algebras4 B% L! D/ s% z1 d: J
Topological groups' O0 E, Q* ?/ [# J7 O* J
Topological spaces* b* y9 u; m8 q
Topological vector spaces8 Z; q4 q& T" ]+ c
Torsion groups
5 u2 f* B v% z' r7 J, u1 e8 NTotally ordered abelian groups, h6 ~- P p0 t6 i/ I6 y
Totally ordered groups- R( |% h! Q8 N: p# I4 t
Totally ordered monoids5 ~. @5 j- k; r7 F2 U4 _% |5 J
Transitive relations
' [5 U& r8 F4 N- tTrees
0 b( c* Q" M( r+ LTournaments9 a/ z9 l, N/ Y9 Y3 X3 N5 E$ h
Unary algebras
, v7 M. t6 x6 QUnique factorization domains
( f* I" j' C6 J0 kUnital rings
& N8 V5 t( X+ B7 l- I. BVector spaces
' ]6 H) F! }/ m4 w! S) TWajsberg algebras3 _0 {+ J9 H2 O
Wajsberg hoops; N% n0 m; i1 x' H% m V
Weakly associative lattices& {5 x4 R1 h" w( ]2 _) Q( ?. m
Weakly associative relation algebras
0 O3 u/ o I f' y: e8 n uWeakly representable relation algebras" r% z( y; G/ y$ C5 T( p9 x
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