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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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% ~* t/ N+ C$ L8 F5 M
4 Y/ K9 |$ t5 ^
Abelian groups Abelian group
; |+ C9 V( k4 @) |/ h7 e& uAbelian lattice-ordered groups5 o4 h! }+ d% \5 o- o+ x: j
Abelian ordered groups; |7 \( c* w6 F2 k$ s
Abelian p-groups
/ w# M% X6 n' U( B" Q f7 n1 hAbelian partially ordered groups" s! x5 G2 ?3 o! H
Action algebras Action algebra& O5 h l& m( t1 g( r
Action lattices
. q0 T9 q6 p+ `Algebraic lattices
! i$ f1 B2 P$ @# D) j" Z# G) dAlgebraic posets Algebraic poset) f9 T- M" }0 F5 K& B
Algebraic semilattices
! ?9 X9 [1 j" i/ Y7 gAllegories Allegory (category theory)& I `$ s% t% |# S, w. c
Almost distributive lattices
0 T4 Q7 u) ^* s; D+ L& VAssociative algebras Associative algebra6 d/ N* q- _3 p& Q o/ `' w: }
Banach spaces Banach space$ q+ {3 a' J& m. x
Bands Band (mathematics), Finite bands
8 m, i& Z: e9 \8 ]% _Basic logic algebras; p3 o9 t6 ]. j- g! t& o9 S* e
BCI-algebras BCI algebra
4 P; {9 @. m/ S6 x' f! aBCK-algebras BCK algebra F% C4 ]" l' y. V' A* E; d2 Y
BCK-join-semilattices
. s' H F1 g& b( Z* zBCK-lattices; e$ H, a6 w/ _
BCK-meet-semilattices
) @9 N! C; ~' p6 M5 C* dBilinear algebras
8 x0 {7 d+ i; g3 ]- gBL-algebras: q3 X4 h8 X3 K7 a$ [1 y5 B0 u, }
Binars, Finite binars, with identity, with zero, with identity and zero, , `5 G$ Q" [9 M- C1 t
Boolean algebras Boolean algebra (structure)
" L3 U3 C# p# ?4 p/ ]Boolean algebras with operators
) x c+ @ T2 G7 v* ?( R, sBoolean groups) f, N$ n0 y: f1 |) k$ D
Boolean lattices& t' w. X. J F
Boolean modules over a relation algebra
/ B+ ]" v3 U: n; h! V5 ^9 TBoolean monoids; Y( s. X0 F+ b; o
Boolean rings
$ l( ?; L1 l1 x8 S7 nBoolean semigroups
* v( I: x L6 S( Z2 d- _Boolean semilattices" E3 S# v& l4 A6 q8 t1 M0 t; g6 M0 D
Boolean spaces+ }5 `% h9 U8 j7 x$ b5 M2 ?; o
Bounded distributive lattices
6 m7 n: P1 e) o. _( Z7 F1 |: c' RBounded lattices: G+ H+ o3 x# R6 t# c( M+ X
Bounded residuated lattices, s' B5 m3 {5 @9 N2 o% Q! Z
Brouwerian algebras7 c/ {9 F% v* x5 b5 j# y
Brouwerian semilattices3 b. M4 e. G. I" G; W+ n, P
C*-algebras' ~0 t+ m7 d+ n/ h# I2 Q
Cancellative commutative monoids
6 f: @7 V- ]3 @! X3 `- I3 j% h9 q3 gCancellative commutative semigroups
% S1 [6 g6 m9 d5 ?Cancellative monoids
6 Z; a% x1 C3 [" E: d. MCancellative semigroups
( c" V4 ?4 Y+ s, I$ S2 ` j6 oCancellative residuated lattices- u( x* ]/ H+ U
Categories; U& _8 N8 C0 Y( @8 f, C/ T5 ?" p
Chains
" x5 i& d* ~3 Y- ^Clifford semigroups" X z. G5 F! e) @5 A5 v# B
Clifford algebras5 h1 x0 ~' @, q
Closure algebras
4 ^ O2 R3 x3 ~6 b% mCommutative BCK-algebras: L' L! I) [3 E9 W' [
Commutative binars, Finite commutative binars, with identity, with zero, with identity and zero ( ~: y% _6 R/ w' b4 O3 i
commutative integral ordered monoids, finite commutative integral ordered monoids
& { t o0 f; JCommutative inverse semigroups
4 r/ N2 }0 k& W' f4 KCommutative lattice-ordered monoids
0 h4 L7 |4 E* }/ SCommutative lattice-ordered rings( q3 E; f2 U& g" R- b
Commutative lattice-ordered semigroups$ X9 O- w7 U8 r5 ?3 ~7 _" J$ ?
Commutative monoids, Finite commutative monoids, Finite commutative monoids with zero
+ j4 B# l) E% L' O8 v- ]( N0 R2 ZCommutative ordered monoids' C7 S. T2 F" R, j3 V; d& \) K6 z6 ?
Commutative ordered rings( q9 t: ^5 c* L3 p, I, i( L1 \
Commutative ordered semigroups, Finite commutative ordered semigroups
5 y/ a5 M7 M" s' Z9 h; VCommutative partially ordered monoids3 p' X8 l& ]' M# U7 u5 r
Commutative partially ordered semigroups4 H( K% ~) I5 k" I+ Y( y
Commutative regular rings" e. i4 a- P, J- r
Commutative residuated lattice-ordered semigroups
/ l! O8 |# |; d9 aCommutative residuated lattices
* y% K/ u' t$ i% Y L$ Q8 {Commutative residuated partially ordered monoids5 K1 N9 U, U' N. b( @4 C
Commutative residuated partially ordered semigroups
5 B$ H9 e1 l; T9 iCommutative rings
+ h. Z: ]$ p4 y% [4 v6 c, _Commutative rings with identity* d' y8 s2 w7 l9 _1 y# f3 R% d; c; C) @; i
Commutative semigroups, Finite commutative semigroups, with zero
* u4 ^/ E( ]& o3 yCompact topological spaces
% n" _4 W2 I! JCompact zero-dimensional Hausdorff spaces
8 ?1 \4 q- A0 }% S i$ YComplemented lattices
, ^- G$ H) c" `7 `; s, ^Complemented distributive lattices
- r; J% w# H' K |) oComplemented modular lattices
: x! u) U4 U4 K. p4 [Complete distributive lattices
, L/ C$ M* k u* Y. T5 iComplete lattices
: F E u: h, E; K% m; jComplete semilattices- r7 ^9 k. h9 X$ V' q4 k# c
Complete partial orders
$ R$ l z0 x2 r f' B* H, yCompletely regular Hausdorff spaces
( x' P: R) V3 m/ Y! U' o; _Completely regular semigroups: B& Z* y) ^0 r9 Q
Continuous lattices- Y. j* j; L) y% t; k& W2 C
Continuous posets8 b1 i; y- J# |( T) `
Cylindric algebras. w6 u: B+ Y" a
De Morgan algebras. g' h. J8 N q2 N$ F( y
De Morgan monoids q2 E; M5 q- e- _. ?
Dedekind categories% j5 d H! K$ i: L- B' z& F
Dedekind domains! j# N& T7 p, m* @' w1 ^# {
Dense linear orders
4 z9 a/ ~+ \- f0 K5 cDigraph algebras
v3 t& ?4 y1 i) o& ADirected complete partial orders! |; z& h+ p1 F
Directed partial orders
/ \- u3 o# d" Q: FDirected graphs
! F) f: \) `1 g% c3 D7 d/ j* dDirectoids
9 `1 r2 D' p3 HDistributive allegories
0 T' O2 n( C5 ?, }2 V2 l, ^: J- o% xDistributive double p-algebras
4 T7 r! J. `) }" lDistributive dual p-algebras
0 C0 y$ [' G) EDistributive lattice expansions+ i: B. j4 r7 w! H* ~+ D+ R
Distributive lattices
, v; G9 w! l4 a* `1 sDistributive lattices with operators% D0 ?7 q$ S# `0 D2 S/ A+ u0 t& c
Distributive lattice ordered semigroups
, X; d, J$ l* X* K1 [2 D4 y) hDistributive p-algebras
( J- B0 ^8 l6 s. }3 i1 H( J) xDistributive residuated lattices
_3 A5 G v; ]' V/ ^3 WDivision algebras* u7 G3 j6 c1 W( u( g: z. E9 O
Division rings
' U# Q. g2 j% B; Q1 FDouble Stone algebras/ V" J: r. l: _1 I( g& k
Dunn monoids4 ~$ V6 Y }2 O0 N0 m* E; Y. |
Dynamic algebras" ]" Y: p: N' ~4 P9 n
Entropic groupoids
N3 e2 }2 r# I; \Equivalence algebras* A3 W4 Z* B2 E' p5 {& b* _. ~
Equivalence relations
; W: i( E6 o1 w @; l; y6 H& X5 tEuclidean domains1 ]5 v2 s( u" |' P6 a8 ]/ d6 Z
f-rings
4 U) l/ Y- _, N3 ?Fields9 }4 x0 E) m) H5 y- }+ G" Y
FL-algebras. w4 m, G& L1 {* D% d
FLc-algebras) |& K7 N( w+ ?& e. J% ~* k! g
FLe-algebras
! k2 S8 F c( c- z; ]" PFLew-algebras, M+ ?4 T' a. k" `& U: r
FLw-algebras3 C* D) J# d' b% l4 r
Frames
1 i$ c, Y' \, W! jFunction rings4 B6 G% j* p' p4 q
G-sets
8 k; v5 ~9 c+ Z$ eGeneralized BL-algebras0 [8 V1 n* Z# j
Generalized Boolean algebras
+ X# S8 h" J7 `Generalized MV-algebras
3 f. ~# k9 Y# [) A6 x, ]Goedel algebras2 ^" _$ P- e" N0 ]2 r
Graphs/ M# c: u( T, K( Z
Groupoids
: e- E' ?! e* F! nGroups
; ?) u0 }1 f5 t# M7 E. JHausdorff spaces5 e. ?6 J- H1 S* h
Heyting algebras
: t% u1 @" X1 k; d/ h( NHilbert algebras
1 {" ~* Z. P: l: k$ ~Hilbert spaces. o' f; w& F4 q4 r3 M) i. p6 f
Hoops
( T6 R% m- {* X- j5 `Idempotent semirings
: l. K# Y5 f3 wIdempotent semirings with identity
6 M8 X( r- a ?5 N3 u+ [/ A9 LIdempotent semirings with identity and zero
! o$ ?2 m6 n5 A. oIdempotent semirings with zero: ]6 w5 x5 P( G
Implication algebras
4 [& Y9 ^( P p5 ^( r8 a5 MImplicative lattices ^5 l4 g& L3 y& Q+ Q9 i5 X
Integral domains% i" R* I/ O3 V; i
Integral ordered monoids, finite integral ordered monoids" i8 e7 l/ w" B' p
Integral relation algebras
/ K7 ?3 q4 z1 B) l5 nIntegral residuated lattices
8 E# @6 G* a$ J. c+ gIntuitionistic linear logic algebras
8 l: L+ \0 o7 M! `, Z) A* }8 RInverse semigroups
# o1 a; b! r8 Q, S4 Z: sInvolutive lattices
# K$ x- o% l" N; t9 u" ?Involutive residuated lattices" z& V8 {( N$ v1 L5 _% C6 |2 C
Join-semidistributive lattices
, B, _+ \% a% f0 @Join-semilattices: y) R" u5 O7 ~: h2 M7 K
Jordan algebras
: g* C7 H8 t9 J; L% |, G9 T6 tKleene algebras
+ y6 g2 J8 n# P$ rKleene lattices
6 E( C1 I" _" cLambek algebras
/ G* L; c( D* {6 OLattice-ordered groups
7 L3 O/ ]& j& B" ?% `Lattice-ordered monoids
7 D7 q5 ~* P% ?0 E8 ?Lattice-ordered rings
/ |* u% v& n* kLattice-ordered semigroups
0 J; |+ o! C) i0 ~; WLattices6 |& a: G7 y8 ?, x7 L0 U+ t
Left cancellative semigroups' y5 H! B& B) M( l) ~
Lie algebras
* R& u$ q8 O: W( c# ?* eLinear Heyting algebras
3 Q/ a2 m$ W$ n) F4 y2 t2 OLinear logic algebras
* g9 ^+ B1 ?& q: ] tLinear orders4 _. H- M4 d1 A% ~2 n
Locales
4 W0 P$ T% ]) H% G) sLocally compact topological spaces
8 z/ M4 t2 T9 t0 U5 u" I) KLoops% Q+ R% @8 Y8 g1 s2 I4 y
Lukasiewicz algebras of order n
" K. M" X3 i( Z3 Z( c JM-sets
8 _( ^: E2 ]( [Medial groupoids
% C+ c6 m; S& u E: o+ L$ f7 |/ q- u4 cMedial quasigroups
4 c* _* M) e2 Y7 o9 W5 x1 r$ GMeet-semidistributive lattices
" B& m% X0 e& V$ c) JMeet-semilattices
9 v- G, _, N% t5 X1 f- V+ ~, Z4 m# z$ qMetric spaces7 ~) K) F' G. K* Z" `9 ~; D
Modal algebras
; e3 F) ~' c) l+ nModular lattices
7 c! I- J. Y C7 x+ UModular ortholattices K) K( R* h6 m
Modules over a ring9 B# Y4 a0 R% U' _' r& S
Monadic algebras
* c: [" ^0 G9 c4 }+ O/ z1 \Monoidal t-norm logic algebras# \- d& b! E; J4 Z
Monoids, Finite monoids, with zero7 A* u$ R- C7 Y+ [ Q# V
Moufang loops
% L. n6 p# {. E$ ]" q: r! DMoufang quasigroups
: O+ ?. n( \9 R- FMultiplicative additive linear logic algebras
& l h# h) ]- u2 p( vMultiplicative lattices
' J/ `" T4 Q8 T1 k; P: D V; f; m6 m! PMultiplicative semilattices, U# a8 ]3 \8 H5 e9 P5 d6 t
Multisets% H5 p g9 f3 q1 N, d
MV-algebras( y) g" b) y0 z0 O3 R
Neardistributive lattices
4 P( T) d- }4 _* L4 `. KNear-rings! I5 E0 v! o9 g q# |% J
Near-rings with identity
) |& V2 u+ C1 E# r+ @% Z9 F9 W- fNear-fields3 C/ i9 R% V' s$ L4 s
Nilpotent groups/ ?, B' Y$ C/ a0 q# [7 ?0 @+ ~; j
Nonassociative relation algebras
1 |, z% H- K% p T2 @& V- fNonassociative algebras* G: A8 R8 M: L* {* N8 c
Normal bands
8 H1 |' ^4 M3 y, N k! X+ W* pNormal valued lattice-ordered groups( v, j. f3 p/ U3 Z
Normed vector spaces
4 j# H, Q. u8 f7 DOckham algebras
6 ~8 t' @8 m) H0 A5 R. }; ~Order algebras
, H' u+ @: S7 e4 e2 POrdered abelian groups
/ A9 S5 s, _$ k3 uOrdered fields
( f; f2 Z! I4 |0 SOrdered groups
, N/ E, A9 E1 I; e! Q2 rOrdered monoids7 b0 n" b3 K' s0 _5 Z
Ordered monoids with zero
: t ?) k" t/ H, zOrdered rings: \3 r( x. g0 z) M
Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero- I) o4 n2 S5 z' l
Ordered semilattices, Finite ordered semilattices
2 X$ o4 F/ P0 _7 JOrdered sets
" x$ ]; [9 ?; d( V1 fOre domains
% D! U" E _0 G8 R3 c" mOrtholattices
/ g! B$ ^! f( [Orthomodular lattices) c: z J3 R. ?$ V% M- Y& h: r
p-groups7 G& m& ?8 y# b- T# ~% R6 p! V* f
Partial groupoids; d0 H% b" A7 y# ?. I
Partial semigroups! Z' L8 `; V" g6 a# V- |
Partially ordered groups
! _0 [! }$ J Y" qPartially ordered monoids+ X/ I4 B9 E5 Y* C
Partially ordered semigroups5 c2 a8 N2 M7 W, D6 S
Partially ordered sets
; P7 y# G3 L; N# L: yPeirce algebras8 l+ |4 V5 d' i- Z( B" X5 W/ g
Pocrims: e( t; d& H: D
Pointed residuated lattices$ E5 [8 B. J7 W% D8 }5 X o$ W' ]
Polrims
3 Q8 e) d/ r# `6 R+ ePolyadic algebras$ h z$ J* L8 E6 ~" a M5 L: t
Posets
: S8 g9 P7 x1 o, D& J* T# [Post algebras
% S; Y% R3 X# _- N+ Y" a, w# qPreordered sets; h' Y C0 x, Q2 H1 B
Priestley spaces) h4 t% {3 i8 w# x7 M! @3 A1 E
Principal Ideal Domains
& [1 S7 b/ ^2 C1 E) ~2 zProcess algebras
! G" `) Y# k) o/ gPseudo basic logic algebras
: M1 O- F9 v% g: e" I- DPseudo MTL-algebras
( ~+ F( Q8 U- n( ~Pseudo MV-algebras
7 a8 s! E3 f, C' @/ \; qPseudocomplemented distributive lattices# p2 O j& G6 x) w" y
Pure discriminator algebras" N4 u) T& I5 P s; W5 U& A; q* Y
Quantales
h) U6 P4 V" h, J: NQuasigroups
9 p$ l4 I3 S' R8 }8 K/ IQuasi-implication algebras
* c. i1 c/ \& B& n& T0 u' X6 aQuasi-MV-algebra
4 R- y5 h' Y' }; J. a% ZQuasi-ordered sets
) ?) v% s+ z# u! xQuasitrivial groupoids1 D5 U" `0 z% o9 r2 n3 w
Rectangular bands+ T1 ` h; H& G! Y' R6 Y6 e& ?
Reflexive relations* I$ ` q( ]2 G0 l: E
Regular rings/ d. ~& g' b9 B7 D; t3 _
Regular semigroups
* }% l" {4 z/ k* e. xRelation algebras# G+ s$ t$ }" V7 a9 n8 s
Relative Stone algebras8 e$ ?( t* }' ^6 H: ^6 g
Relativized relation algebras2 B' p' A W, Z9 p. M; `
Representable cylindric algebras
( a/ e7 S& p$ }- N0 O8 r5 ~Representable lattice-ordered groups* P0 P" y! ]* `. B) Y$ l0 P
Representable relation algebras
# w7 S' v1 h/ gRepresentable residuated lattices
0 N% n0 d; ^: \5 g- i% Y6 dResiduated idempotent semirings
0 `4 C! U' P5 v! Y: k7 v- s0 NResiduated lattice-ordered semigroups
& L5 h: l" g U4 E' lResiduated lattices
: O y( y5 [) U1 S: H( j" Q7 IResiduated partially ordered monoids9 b3 L+ a( h# K0 l% b3 w, Y; h
Residuated partially ordered semigroups
8 A9 d3 j* E' K, P) eRings
+ ~, K+ \' d2 e N) g7 uRings with identity& I$ p. M/ ^ s! m( v1 Y! n
Schroeder categories
$ @& M1 @, O3 ?Semiassociative relation algebras: c, M5 D; _" a9 ]4 c3 a( f
Semidistributive lattices4 {4 p1 j; J9 ^: i
Semigroups, Finite semigroups7 c: `" o; B" F- [
Semigroups with identity2 K8 j1 l) e: W6 l# {
Semigroups with zero, Finite semigroups with zero& w4 T! r; D0 }: S2 P% ^# I
Semilattices, Finite semilattices. t" t2 O$ G; B2 _
Semilattices with identity, Finite semilattices with identity9 t1 v D0 m# y+ |& L- v5 d# d
Semilattices with zero9 |- E* j: {! r( P. N+ a5 k' d
Semirings
- a( j+ Q+ D% Z4 q4 t7 QSemirings with identity; P8 ~: W+ R, ]0 ?, n6 t
Semirings with identity and zero
1 Q; a( W3 M0 Z6 s- m: `Semirings with zero! C7 y! m& t2 |( L
Sequential algebras+ S3 F/ s5 O6 Y4 Z
Sets4 [+ l7 ~* B' F8 F
Shells
# o6 l; P- N5 ]4 C' w/ K( eSkew-fields
, U( d& U [% I9 Z B. t8 vSkew_lattices! Z+ {2 B+ D, `1 {/ K l
Small categories# i/ l1 W) P) ^+ N* k. q$ k3 J
Sober T0-spaces
$ l8 K( @7 z WSolvable groups
; |% o: o+ k8 D7 nSqrt-quasi-MV-algebras
/ \& M a; J3 \Stably compact spaces, `+ k* f! s7 [
Steiner quasigroups% K! }2 R4 o5 I+ ?+ Y4 I+ e0 @
Stone algebras! i" k) n) w2 t& a7 X
Symmetric relations
9 }+ }$ s% v5 PT0-spaces7 ?+ u: ?6 x# ~: k) q/ O' F
T1-spaces
8 h/ I: o% | I) D# ]T2-spaces$ Y, C6 l% @( o' D3 _7 l
Tarski algebras$ r% ]* ?% |8 _
Tense algebras( F3 C* ` W1 S9 e
Temporal algebras
# k, u! q$ g6 J: U: GTopological groups
P9 \1 S& ?# h& ^ v x' ~2 k2 N4 OTopological spaces* `5 [: g) _! M+ k% j- M+ M: ], K
Topological vector spaces2 ^% C" E& Q) m: }# R2 W4 D2 y# [, M
Torsion groups7 r6 g; q6 o% w5 l% D! q9 f6 S6 N* g! [
Totally ordered abelian groups' n, H; x- }! S
Totally ordered groups
' D8 U" g$ }# t$ STotally ordered monoids% w! u& T6 u/ P& P7 S" Z
Transitive relations
' r0 U8 |1 W. g7 [! k i6 RTrees
5 @3 c+ B/ b* l, l# HTournaments2 W" }- m) _' M4 q9 |; y8 R5 G) j
Unary algebras2 D! |& r+ b7 d1 y2 R0 ]5 w2 @' ~
Unique factorization domains$ W4 Y$ K6 f0 u3 P) w
Unital rings2 G& O" U3 J) o$ h! K [
Vector spaces
3 I) _4 V4 h* {: a( h1 ~/ @- dWajsberg algebras$ \( p0 R% r% H( e$ b+ o
Wajsberg hoops
( ?4 X+ ~8 w9 D7 {& ?7 bWeakly associative lattices
- v( M6 W# B! ^ t* p% e2 w+ jWeakly associative relation algebras- o* K/ d5 x. H, A, M0 I# g
Weakly representable relation algebras
' w. o: |3 Y9 m |
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