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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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; j0 O0 a# L# c, d) m2 a$ G; A5 Q7 q& E
Abelian groups Abelian group
- {5 c" f7 R0 I5 C6 r. v- R$ `/ z# d0 NAbelian lattice-ordered groups" ~6 S1 |# Q& R0 }" \
Abelian ordered groups
; P( S% c9 y3 Y7 Y" ^, HAbelian p-groups
3 J1 R$ D4 W S/ o/ G4 jAbelian partially ordered groups% b0 g1 p& ^! s6 w- ?
Action algebras Action algebra
2 m. U6 l+ a* n: gAction lattices& m* U7 s' ^; {3 z( n) X _0 Q
Algebraic lattices% U" r5 d N& v% t l
Algebraic posets Algebraic poset" S; q0 W- j) {: u8 q; h5 L, D) ^! u
Algebraic semilattices
1 a$ t) ]) Q' t$ rAllegories Allegory (category theory)
2 Y" g8 I3 n' I; R6 VAlmost distributive lattices
f7 I8 y* c/ X( v; D/ e. j( AAssociative algebras Associative algebra. L8 c N" [+ @
Banach spaces Banach space
( H7 A8 l, _1 M+ ^+ N, kBands Band (mathematics), Finite bands
# f0 }+ d& k- @# aBasic logic algebras) |) I# G y; F8 ]: U& M
BCI-algebras BCI algebra
( O$ X0 O6 O" d) lBCK-algebras BCK algebra
2 p& t% T) v; {2 A6 h9 l4 s fBCK-join-semilattices
( [$ ~( M8 U& i2 ~' ^BCK-lattices- ^" R0 q1 _1 k: r6 s
BCK-meet-semilattices, G1 k4 E- p* m0 D0 e6 C; s6 q
Bilinear algebras
- {) K4 Q1 ~8 K8 \: N d9 l& bBL-algebras" F. z- n) A: ?$ p% M3 q
Binars, Finite binars, with identity, with zero, with identity and zero,
! H7 g; O2 S$ J7 W8 Z9 I, uBoolean algebras Boolean algebra (structure)
1 A* }" Y4 |: KBoolean algebras with operators+ p) S9 X1 n. ?- w# u5 K& S, _
Boolean groups% s# P3 ?+ e4 L G8 G
Boolean lattices% {3 Y. z4 J9 J8 N. o
Boolean modules over a relation algebra
9 z1 i$ K" T- A, o sBoolean monoids
, S% }2 C& H" L( {Boolean rings
]) F6 m; a$ G, f, E8 J0 QBoolean semigroups
3 e _+ N( u' Z- A3 q* nBoolean semilattices
- M/ x* _0 h. f/ bBoolean spaces6 u+ e/ o6 i0 f
Bounded distributive lattices
. f8 u2 F7 q) Z; b( H: MBounded lattices
$ i% S1 s5 w0 }3 qBounded residuated lattices
2 E7 ]; G8 P6 sBrouwerian algebras' J; m- h" q! G
Brouwerian semilattices) F2 P" M! M! |- c# Q6 {+ r6 t
C*-algebras
5 {% h& D; G9 C1 J2 sCancellative commutative monoids
; B) ]( o3 p. t A ICancellative commutative semigroups
0 u6 _5 a1 U8 U7 DCancellative monoids
8 [: }# {8 u7 @# x% g4 sCancellative semigroups3 B0 f; v+ J, i7 Q: T r
Cancellative residuated lattices
: c/ X% [! w. F6 q" MCategories
$ ]7 o" i0 z" Q: q/ }Chains
, O8 @8 M% m! h3 V+ y/ R7 W: wClifford semigroups
% r/ e7 @+ a- Q0 B/ X7 D0 }Clifford algebras) I2 h$ I/ W' }
Closure algebras3 l# p6 p, V @6 e& G
Commutative BCK-algebras8 A& S+ R7 o1 \* N; a8 P
Commutative binars, Finite commutative binars, with identity, with zero, with identity and zero 2 B' I! t9 G }! P! k, b
commutative integral ordered monoids, finite commutative integral ordered monoids
4 G4 a: t# f2 a' JCommutative inverse semigroups! X7 B4 k; k5 p; p
Commutative lattice-ordered monoids% y. c5 ~- W! t M) F4 S
Commutative lattice-ordered rings; y& B: }% P2 ^4 R- k
Commutative lattice-ordered semigroups
5 ]! r$ I0 _) h5 u0 Y8 O/ U8 JCommutative monoids, Finite commutative monoids, Finite commutative monoids with zero
; u5 ^1 m0 b6 A% S; iCommutative ordered monoids9 r/ Q/ @& c( n6 S7 @; d, g
Commutative ordered rings
# M$ |7 o8 S1 X3 w7 n/ n" oCommutative ordered semigroups, Finite commutative ordered semigroups" ]# U4 @2 ^; r$ O5 {
Commutative partially ordered monoids% ~& \3 A" g/ l0 W
Commutative partially ordered semigroups
1 b6 o7 l8 F9 _$ ~3 ?Commutative regular rings* z- z$ ?' h! Z1 D, W$ q8 e
Commutative residuated lattice-ordered semigroups$ w* K" x3 ~" \ B. o* }/ i' ^$ I
Commutative residuated lattices
( h! ^" P U7 \4 Z. J' eCommutative residuated partially ordered monoids
9 W/ _. ~* {+ _4 {* aCommutative residuated partially ordered semigroups
* T1 Y7 _! E) ?( DCommutative rings
& l0 y) W/ x/ sCommutative rings with identity
' a' }8 }4 Y% {( n OCommutative semigroups, Finite commutative semigroups, with zero/ g1 M1 [" }* E
Compact topological spaces
: c" `4 ~8 T: N+ qCompact zero-dimensional Hausdorff spaces
2 u$ v4 i- g6 x; F" zComplemented lattices
, ], E9 J: @1 `6 z1 x' i2 HComplemented distributive lattices
: d o+ n1 u8 }. j- e* o* Q1 h+ m/ wComplemented modular lattices- H- t7 Z; ~) e5 u d. J
Complete distributive lattices: ^5 Y; ~# a% U7 \4 y8 ~
Complete lattices
- U4 y, G- W+ T) s$ V: n6 H/ S* eComplete semilattices N; W1 V& Z5 l+ E
Complete partial orders, m: A4 s, q) A* P* O6 q% n4 G
Completely regular Hausdorff spaces$ q# z( j+ G3 n- S* u
Completely regular semigroups
% ~0 S* X2 A5 _ D' n7 ?- {/ R7 DContinuous lattices
7 L. h) I$ h( F+ s1 }Continuous posets4 z8 N1 F# F- d- P; t3 \1 `
Cylindric algebras
2 v" T, h# T% ^. j, u% xDe Morgan algebras
4 x% {/ J1 K* T$ G4 h. g! `De Morgan monoids1 ^ ]4 U( T5 e3 q
Dedekind categories
& \1 V) L. s4 U1 z% F5 S/ `( f# I$ b1 m& EDedekind domains; r/ W! S/ d1 U7 V4 ?( ~. T. ?7 S+ Y
Dense linear orders
1 g! U6 r5 ?! d/ Q% R; CDigraph algebras) P2 p" k, |# u8 l1 l: K
Directed complete partial orders) L! t; v6 a% Y+ ?" H' |
Directed partial orders
9 M- T" u) V0 w! i! Q* ?/ J! K3 wDirected graphs
& `2 @5 u3 a6 H5 _1 kDirectoids
2 e. O: f3 C# d, U! HDistributive allegories
6 T" h! X' E' y% ADistributive double p-algebras
0 {! O( u4 d2 @5 M* fDistributive dual p-algebras" X, l+ |- p8 N5 n0 U
Distributive lattice expansions+ u. f0 }0 c/ N3 W* |: g
Distributive lattices {, z, }3 r# J9 b' f3 I
Distributive lattices with operators
) o6 p: q% Q J! g0 k6 R5 F, \Distributive lattice ordered semigroups
0 |$ a0 T H1 [& D: j+ S: RDistributive p-algebras
& @$ e7 x' d4 X" MDistributive residuated lattices
O5 O: v9 l( N9 A" rDivision algebras/ T5 |' @+ t' v- l
Division rings$ ]5 i) j# g) B' U" `9 r& }
Double Stone algebras
3 i* O+ X6 I' B; D; ~Dunn monoids
) ~* v; Y$ W3 T. R6 x* x8 i4 T" r, hDynamic algebras" h U4 r! i" q/ a: _
Entropic groupoids
9 _0 E7 i' N- O6 h; n% REquivalence algebras
( W0 o2 {3 h& ]( y+ SEquivalence relations7 R7 j) u7 f4 I4 B$ ?: D
Euclidean domains
2 Z$ h! G3 ], `$ M/ Y( l/ tf-rings: d/ i/ L8 ?& M1 E$ a
Fields0 ?2 G0 h' x5 L: h8 ?6 {: B
FL-algebras
1 L: P% A3 `- b4 n1 x. ?FLc-algebras$ N: v7 R- d6 q
FLe-algebras* x8 a7 F7 u' q# F* j: t
FLew-algebras& s* L& Y/ L' k s
FLw-algebras, k* j5 w4 T& k3 q( J
Frames! i1 j2 B* s- |4 H
Function rings y8 m) w! U! P. H# D8 s
G-sets
) t! u m' [7 a. \1 _3 @Generalized BL-algebras6 g+ s2 p- l& _* ^) I2 \
Generalized Boolean algebras
2 O8 V- l# O7 Y5 U3 A+ l) n6 [9 WGeneralized MV-algebras
8 u4 I; u& E I# U8 w% _Goedel algebras0 i% F( g8 F- ~+ g, F8 ?9 N9 }7 y
Graphs
$ Q! S M, [1 M6 h A' J7 OGroupoids
9 E0 W$ g3 K) y+ n7 ZGroups! i$ l/ g/ R' Y7 d
Hausdorff spaces
6 O2 @* C) i. F$ AHeyting algebras" Y) {; p5 d7 P9 X/ Y
Hilbert algebras: u* P" x. w7 n' q& G2 D
Hilbert spaces
5 h. W2 N6 h4 FHoops
4 p2 D% j$ w HIdempotent semirings
2 s' J5 F T: b4 d8 E1 t* z) n) nIdempotent semirings with identity6 W% O9 L! H2 A+ e( `1 G
Idempotent semirings with identity and zero
" z( Q- M7 t; }& F JIdempotent semirings with zero
% U7 N/ a9 b x) C" g/ jImplication algebras% X, A/ }8 ]8 v1 I( d' Y/ \1 n2 v' Y
Implicative lattices7 q: p6 [* l" N: u2 o9 c# D
Integral domains
/ h# f5 Y+ X& R2 HIntegral ordered monoids, finite integral ordered monoids
, Z+ q1 R( ]( ?3 W9 gIntegral relation algebras
1 p/ Z* u! x5 e: l9 YIntegral residuated lattices, u# _' _+ ^2 z) [9 J
Intuitionistic linear logic algebras
. u2 \$ T, ^' I$ B9 |! SInverse semigroups
) n/ q' a6 f. p' [$ BInvolutive lattices. u/ @! `: g6 c, y# h; B4 W; h7 C" Y6 [
Involutive residuated lattices
$ S; O7 [& ?) k, U9 GJoin-semidistributive lattices) W' Q1 R2 I. s& d# t7 I5 ~
Join-semilattices6 g8 v& E6 ^1 J3 b; w# H
Jordan algebras
/ p' P' U/ n+ m% RKleene algebras
( D3 q1 r2 E9 w! ?1 s. y9 v9 s2 S+ mKleene lattices
1 M5 X4 m" |3 J" Q/ t1 jLambek algebras7 ~; @# C' y u4 P2 L1 o5 U+ M% w
Lattice-ordered groups
* h( V7 Q4 y; g9 ^! Y$ dLattice-ordered monoids
3 T8 _; F/ `% ]/ d2 U# BLattice-ordered rings/ |- l" q6 {- }8 }5 X2 [0 t
Lattice-ordered semigroups0 h& _9 O$ o, q9 ^4 {# M
Lattices$ j5 L/ Y; o9 S A
Left cancellative semigroups) n' R1 B- z1 ~8 L t& {. n
Lie algebras0 R6 g( O8 a( h$ G8 X, V* F
Linear Heyting algebras. X0 Q2 N+ q. a5 `& J. k
Linear logic algebras
0 J- l: P& X7 f/ X7 G& U' QLinear orders9 J% f( b; K# w6 X
Locales
& ^9 H$ e$ f4 zLocally compact topological spaces
M+ N, {9 s3 _9 R/ p" kLoops& v( |' l Y+ y$ T7 i p: ^' r9 K
Lukasiewicz algebras of order n ] v$ I% h2 f
M-sets
5 h$ j0 q( t. ~- R* z G" I) Q8 ^( EMedial groupoids
! l& Q$ h9 T! K2 A/ Y7 EMedial quasigroups
2 @0 e2 J% N b/ `0 sMeet-semidistributive lattices5 K' B3 T0 r' l6 x
Meet-semilattices6 n& v" K- ~! o4 b% m
Metric spaces- Z, h6 L; D- Y9 ?# r* D
Modal algebras% Z4 b# I1 l7 i: l$ b; G
Modular lattices2 v& d- z* y' i: n" q) f: s
Modular ortholattices7 R T% l; V) {+ J1 Y
Modules over a ring- k2 D1 B$ F& a) c4 f& C+ D
Monadic algebras8 k- [3 @/ w" I; H
Monoidal t-norm logic algebras/ A1 F: {0 w/ L' i- y
Monoids, Finite monoids, with zero& R3 t' t+ N/ q2 p) ~
Moufang loops
- [8 J* x" c2 i. {' e" e1 uMoufang quasigroups
( X/ x& w# B* S4 a* B& @) ~Multiplicative additive linear logic algebras
/ O4 \! Y: x0 N) J! kMultiplicative lattices
/ J! ?& _9 |0 k: ZMultiplicative semilattices1 F) ]6 q; ?( e7 g: j! i$ s
Multisets
) N) W1 k0 ^9 v2 i, h9 FMV-algebras
G4 x! A! Q9 H3 V0 D: ONeardistributive lattices3 g9 A$ B# V# E% e7 t9 @7 ?5 B
Near-rings
/ G% \5 _/ y8 S6 l- o8 ONear-rings with identity
5 y/ Q7 z8 P' {1 s: r$ O, V: i, yNear-fields
# x- a3 G. o* `+ YNilpotent groups
# u( z+ c3 r+ L% T1 O$ O i. @! xNonassociative relation algebras% m! D" ` j& h W
Nonassociative algebras# M! w& E3 L, @& s; q
Normal bands
! |: Y1 ]& j9 F, y( G" LNormal valued lattice-ordered groups
) F% n) O2 F$ F$ ]0 r4 PNormed vector spaces8 O; ~* k2 U/ r: d% ~5 t7 f
Ockham algebras
/ w) }+ Z2 b, N, V) vOrder algebras. [- H# z! B- V' h: T7 Y* k7 C4 T
Ordered abelian groups
% X1 V0 ^5 ?$ ]/ `Ordered fields# h T1 x* X) F! A; n2 K* _* n9 W
Ordered groups
( k4 x4 i1 s4 F3 d" _/ z0 fOrdered monoids& w4 D) @- \. u' z( p- C# `4 }1 r: O
Ordered monoids with zero! a* Q, O4 x5 J6 y
Ordered rings) {( |, S# C% w7 l
Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero
2 ^: x3 C Z* W" ~( G0 y& \9 NOrdered semilattices, Finite ordered semilattices; I) Y! F" h* V' f& T% Z3 @. s
Ordered sets
" z0 v" v1 _8 J7 A8 hOre domains: N( s. o0 l) g3 d
Ortholattices
- [) Z0 F$ }' r% B5 w* b) z; ]Orthomodular lattices
2 {9 f" z9 T0 V3 N; M" hp-groups% t p0 f3 X* @% W% U) M
Partial groupoids/ w2 y. g1 @) {" k
Partial semigroups
4 b) B/ \1 l) G2 |Partially ordered groups
$ h2 l' N; m6 C5 _Partially ordered monoids
/ \" q8 H" z% F+ G' BPartially ordered semigroups) F: i+ q/ {" k
Partially ordered sets
- }5 @* \% q! B R' {Peirce algebras
' r* n* a- p: D; m6 t* X6 ^) @Pocrims
& d% |3 t/ S. p) R# Z X6 Y" ?Pointed residuated lattices
$ N, A. M2 P; h' ^Polrims8 b" }- N; B P8 `4 b) |! z
Polyadic algebras; ~" x( s# o& @; L6 _! u
Posets
2 ] R8 t" ]! Z* f, c$ N& xPost algebras
, t7 H9 ~0 a0 E; e7 I2 x/ M3 xPreordered sets9 I( M- j* H6 s! k
Priestley spaces& z9 ?' C4 |8 F! W
Principal Ideal Domains- G3 x6 s% |. J3 G. B* ?3 ~5 l
Process algebras
7 O& y' t0 `4 w# h0 S& x3 X2 {Pseudo basic logic algebras+ l. X5 z# y! o* }0 p
Pseudo MTL-algebras5 i7 F5 q2 T8 \6 E( Q
Pseudo MV-algebras
+ d% z; z" I& y* _4 VPseudocomplemented distributive lattices
, _1 f2 N: ^# l' u1 V9 L; [Pure discriminator algebras/ V7 q. f) l( l
Quantales
/ L: M' r$ o( x. J% z4 ^6 g6 ^Quasigroups
1 I+ {0 h) n% r( n$ Q7 o8 xQuasi-implication algebras
- \' ^+ E# }- E1 F0 A8 I4 v3 z& [Quasi-MV-algebra
8 X% h& q# P+ pQuasi-ordered sets% g; J$ q. Q2 F: A
Quasitrivial groupoids
) y& {, ^) E* }" W$ YRectangular bands
& K% A$ I2 ~; DReflexive relations
; T9 V# |0 Q: e6 q- L8 C) \$ C" rRegular rings2 f$ o& d0 x5 Y) x2 F% _
Regular semigroups
* W% U/ f6 n$ V7 h( _8 l3 P$ QRelation algebras
8 o+ b2 K: G( f6 f; ]Relative Stone algebras
2 p K% x$ a$ C' ^3 TRelativized relation algebras
; n8 M% l: O A- G; ~/ m DRepresentable cylindric algebras3 O$ v$ D4 _7 M R: R" ]+ T
Representable lattice-ordered groups& {8 v6 l8 w- U0 @! o+ ]
Representable relation algebras
+ t+ @' v: |5 eRepresentable residuated lattices( C0 o5 b4 k7 {) k) ~) \
Residuated idempotent semirings
g% y8 {7 E9 b- _) uResiduated lattice-ordered semigroups; R0 E, q6 w& u: { }" i4 n
Residuated lattices
2 F$ }; s% h- y( [+ q! sResiduated partially ordered monoids
7 g9 j5 Q: d5 x, AResiduated partially ordered semigroups) O3 L" l. z1 U8 n/ p- |
Rings- n; @1 e) P3 {, k, r! h
Rings with identity
3 T; d b: ^1 }, GSchroeder categories
6 Z2 d$ B8 S5 ~1 p: Z* rSemiassociative relation algebras! G' [: o" h* B A) `7 p% l0 Z
Semidistributive lattices
, Z% f/ `% D! a8 @( {; _4 f1 PSemigroups, Finite semigroups
% G4 w# R% K' \/ u6 mSemigroups with identity9 C5 ]0 q: Q& q$ v# ~+ j9 d
Semigroups with zero, Finite semigroups with zero8 Y! v- n2 `5 P( d
Semilattices, Finite semilattices
) u( i! H7 d- {" F/ y' u- s# S6 K! |& nSemilattices with identity, Finite semilattices with identity+ |! P" J- g) ^ i
Semilattices with zero
) R! n, {$ Y+ [* F+ {: i- Y% \Semirings6 l* B+ g/ a/ S+ A
Semirings with identity
6 ^# E L- b4 L: G5 \+ m7 {4 f9 HSemirings with identity and zero* M! }: i( g" G
Semirings with zero) |' h- ?' c5 R( b
Sequential algebras
& `! c O7 K( ^% J9 F: Z% ySets* n' o: w8 g4 ?$ n2 A3 W
Shells- T3 X% d' s' q
Skew-fields
0 i9 `& I0 O9 B3 |2 O' OSkew_lattices
+ O# b5 b* j8 O6 P' XSmall categories
* }1 h' X) N" u* ZSober T0-spaces
* I( ^; }3 d3 a* f: wSolvable groups ~+ d+ l {* d: C) H8 ^0 A! }/ B
Sqrt-quasi-MV-algebras
8 v' f1 }- L! W. n& E% g0 S1 tStably compact spaces
]6 m' M' ` n9 lSteiner quasigroups: U, Q1 Z" t8 o7 p+ `; ]
Stone algebras
9 P" S1 Q: z6 nSymmetric relations U3 X7 Y* c- ~6 \5 M/ z4 A
T0-spaces
: \0 E: Z) T$ n. WT1-spaces% Z3 K8 b# H$ |" y
T2-spaces
2 H9 s7 E, ]6 [, t+ p6 A* gTarski algebras
3 n; v5 H: l; p$ |# t, aTense algebras* i6 P+ H1 z% B/ e1 Y' [9 A+ K% z- G
Temporal algebras
7 ?& m% _# X1 B* S, R# e. u- c' iTopological groups
7 c+ S& m7 p$ B/ V/ ETopological spaces
4 P4 L% r# L4 z, ], G. t) l5 YTopological vector spaces
0 k4 R6 r; H, j3 I# Z0 A9 |Torsion groups& r- `4 s$ r& a" D* o. E, Y
Totally ordered abelian groups
3 y0 m. E, [$ x& L6 e3 k" c5 u8 FTotally ordered groups" V; C1 y* C9 P( U4 A# B
Totally ordered monoids
4 o) W3 m# G# o- K0 l6 }) sTransitive relations7 G. C" s p. A2 N4 r0 {
Trees
+ j7 D/ l: M3 l$ ^2 T! ITournaments
p; L/ y: C% D! \* JUnary algebras
. n6 S6 B; S. y( h. p+ f5 }Unique factorization domains
3 B p. F2 W: @; zUnital rings9 c4 f. M+ J4 D7 b4 U# s
Vector spaces( _. l, s! h, W; F: R2 r+ }$ m! I
Wajsberg algebras( E; J) D0 _. R; ?
Wajsberg hoops2 |5 N4 N* R) N
Weakly associative lattices @; |# \, E7 i7 d" E0 H9 l' K
Weakly associative relation algebras
7 a, Y2 z- l3 r6 O0 h2 R6 WWeakly representable relation algebras! \6 t) f5 h P( ]& B6 g' i {
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