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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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0 `7 b9 p8 V0 b+ _$ p% [; u
) ?* r6 `+ \" M7 {" X; s" K) IAbelian groups Abelian group% e! R9 K& M0 c9 x; }9 n0 V/ ?: b
Abelian lattice-ordered groups8 C a4 u9 O. d; D% ]1 y- }" V
Abelian ordered groups( Z8 e6 h s1 I& n8 G
Abelian p-groups
( ~% g' P2 {& e; [$ s0 }$ VAbelian partially ordered groups
9 C; h, r# ~! F8 h. t& KAction algebras Action algebra
/ \7 Q7 t& {! S& } dAction lattices" e" x9 J' `- B$ j0 i( C
Algebraic lattices
/ z) d; U! o1 X: X$ iAlgebraic posets Algebraic poset
% G6 @( O8 ?8 U5 iAlgebraic semilattices+ k7 s9 g& O1 Z; j6 y& S; t
Allegories Allegory (category theory)
. |8 M. u* K7 T* o: @$ b. XAlmost distributive lattices4 L8 Y* W: P* x, N# D7 x! K
Associative algebras Associative algebra/ v: J! e9 [# G% a v
Banach spaces Banach space1 p; w; [9 b+ q0 |8 W' Z- N! X" g
Bands Band (mathematics), Finite bands& B# a+ r% G a
Basic logic algebras4 x: Z' `: B5 n$ v0 h
BCI-algebras BCI algebra, b ~+ X/ E: E: E9 Z4 j* ?
BCK-algebras BCK algebra' I' z6 ~$ c7 W* A5 g9 I4 ^9 W9 p
BCK-join-semilattices5 P/ {. H, p$ v9 D3 r# d2 d
BCK-lattices
: R& [& x, l3 s; h" t! qBCK-meet-semilattices5 ~' q7 W- W5 c
Bilinear algebras
3 I. |: c7 g( x, O. k* J" NBL-algebras
0 O# S$ R: W: d" C' P" OBinars, Finite binars, with identity, with zero, with identity and zero,
5 l5 ^" p$ Z+ \& R) @2 b" D* zBoolean algebras Boolean algebra (structure)/ s3 D3 o% U- L
Boolean algebras with operators1 v: F! ?0 ]* C( o+ p5 P
Boolean groups
; L1 ?) q' q7 g' d# |Boolean lattices% H4 v$ J% E. m# v- L, d* G6 S
Boolean modules over a relation algebra( i: o, H4 k2 _8 R9 ~' o: j
Boolean monoids( G/ N) S5 O; c$ H& {
Boolean rings- i+ D% y$ @$ ^- G! X
Boolean semigroups
: ?2 c; h$ Q* \; U, w( UBoolean semilattices
& E# e' M! K: [; M7 Z. y0 IBoolean spaces
% v! {* [+ m( i$ rBounded distributive lattices
, \% N7 I* X! R7 a9 _Bounded lattices
# a* W/ a3 [7 A2 X0 ]" }1 ?Bounded residuated lattices
- L5 {4 }: _0 [. P% j. g% aBrouwerian algebras
, ~4 I( j2 q9 S5 y# q. wBrouwerian semilattices7 U3 T9 _$ _. w
C*-algebras+ X" H$ e) ?+ x$ _
Cancellative commutative monoids
5 u- t, v( Z5 H! S: r, Y1 B% \Cancellative commutative semigroups
* s9 U: P8 L: Q" sCancellative monoids
1 o4 l- I1 s# ^; qCancellative semigroups
1 R m& \, G% Z6 q1 `" I) SCancellative residuated lattices% M( t- Y6 e6 s3 F6 x; f2 r6 R5 O7 t o
Categories
5 n( f5 ~" ?, Y! }Chains
: i4 N3 ^5 Y/ x0 w" iClifford semigroups6 A0 H, i/ ~! x9 b8 E- i. l
Clifford algebras4 ?9 G* t! p. Q4 o/ @/ [( b- N
Closure algebras& p% d8 }; O8 ~7 _) ~
Commutative BCK-algebras$ R0 e) p' }/ A, L% e
Commutative binars, Finite commutative binars, with identity, with zero, with identity and zero - R5 X1 F; x1 V2 V2 i# _0 a
commutative integral ordered monoids, finite commutative integral ordered monoids
* v) h$ w6 i6 @6 ~! _Commutative inverse semigroups
- d$ _( E$ n# S3 V, ~3 _7 @Commutative lattice-ordered monoids. E8 ?2 K* ?3 k$ T9 |8 b8 W N0 S
Commutative lattice-ordered rings9 {* z- N* N+ L5 ~
Commutative lattice-ordered semigroups0 Z( z6 z. z/ z/ c) W5 j0 [
Commutative monoids, Finite commutative monoids, Finite commutative monoids with zero/ k) p6 L: Q' [% p" P3 ^3 s3 u/ [
Commutative ordered monoids
8 b: o3 h6 d; o" r* V5 d# I( gCommutative ordered rings
9 I8 U# j; {/ f* b; C) h( TCommutative ordered semigroups, Finite commutative ordered semigroups* r6 {6 v& m6 V3 y; C
Commutative partially ordered monoids3 }7 g, {0 e" a q2 S6 z: N4 h
Commutative partially ordered semigroups
9 z0 F& x/ A j* O7 J2 VCommutative regular rings
' |) F0 T: P) f. C: w5 `Commutative residuated lattice-ordered semigroups2 M2 t8 j* E5 _( ]! i b, ~) D
Commutative residuated lattices
; ?! f0 k. B ^' \2 KCommutative residuated partially ordered monoids
# W: {) Q* c C, E; ZCommutative residuated partially ordered semigroups# g9 l& Z/ ^- e. y* s
Commutative rings9 p3 N% x, l( j6 o u! [' t5 _: G: o5 X
Commutative rings with identity0 t" v1 J; q) [
Commutative semigroups, Finite commutative semigroups, with zero" R' R& c8 M: F) N& ~
Compact topological spaces
4 J0 E/ I7 [: b4 J3 m0 T' d; BCompact zero-dimensional Hausdorff spaces% h/ v0 e3 p' f9 U G5 }
Complemented lattices
. S3 J; Z) g4 d# p9 o$ d- h, WComplemented distributive lattices, n) [7 p( v' [
Complemented modular lattices
# `6 T$ k. r+ |2 NComplete distributive lattices
1 J# b4 b9 A/ s: M |: T2 M" l a+ yComplete lattices! a% Z, |# }; p0 k2 ?1 w" U) q
Complete semilattices
. |8 D( J; v6 ]- p) A) M1 kComplete partial orders5 |. O8 d: M3 Z/ |( m7 z
Completely regular Hausdorff spaces
% _! {" C# w5 S; r# Y. ~, P* I. ]Completely regular semigroups0 C0 k v6 r5 q; U- I
Continuous lattices$ e$ }, V/ W; G4 q7 b
Continuous posets) D2 F6 D% A4 N' L1 t5 `6 m
Cylindric algebras
y( n4 J8 o3 |. r/ h @3 uDe Morgan algebras7 o5 y- @8 m; ~0 E2 E( @
De Morgan monoids' j* B8 y. p1 X: v4 U# ^
Dedekind categories
- V; k- s9 K- t6 J1 DDedekind domains
H8 e c- s- @7 x; @Dense linear orders: n% B/ Z- C+ a/ ~1 ~- D% @" n
Digraph algebras
5 e, `3 |4 U/ ~* E" b$ T; l8 t+ YDirected complete partial orders M# K3 \( G: o' k! t( M4 L7 s, ?
Directed partial orders& Y, S3 H7 B8 Y) S
Directed graphs* h+ q$ w% n' @; V- t
Directoids
+ i; s- x8 L2 z8 S. _Distributive allegories( c3 B- ^& D2 q( ~: b6 B
Distributive double p-algebras
3 Z1 K- v7 _; W) O3 D cDistributive dual p-algebras
4 t) k2 ]: E% h! _: h" D5 @! VDistributive lattice expansions
' @& }. w2 a8 n5 @Distributive lattices
9 i& ], W, ?" p/ h( ]Distributive lattices with operators
5 ~! i; `- a1 e' X6 X) M# n" MDistributive lattice ordered semigroups9 B9 ?2 [# Q7 w' I. l
Distributive p-algebras }, n+ g" H6 f
Distributive residuated lattices. e; S( d+ ]. H& v* C
Division algebras3 H/ n! a l5 m/ M
Division rings
$ z X- ~* I& }3 |. WDouble Stone algebras
8 Y/ u' E4 Q/ E! }8 _# n3 A/ ~Dunn monoids
9 q4 H( ]6 ^7 m% X8 u0 jDynamic algebras
5 I: o5 R7 ~8 SEntropic groupoids- s4 {" G0 I b1 I( R
Equivalence algebras
# e0 L; m( n; d- r/ q/ n, A5 \Equivalence relations
" I9 N c! t) _6 ~# D( i, A& JEuclidean domains
9 g0 ]1 i; m% z, q O0 A# L! Wf-rings1 S2 W# j% I2 ~, r$ J( P
Fields
' A! D, T6 ~* W; K3 C" C6 J" vFL-algebras
. R# p$ n8 B. e$ b/ S9 q2 i# JFLc-algebras
. T. l; z; A" ^2 r4 gFLe-algebras
" C) I4 _2 v. K1 {$ l: u+ v, D6 SFLew-algebras
7 A8 c6 s+ r |: ~5 Y" k! ~/ S2 kFLw-algebras5 Y# m" m7 s; A7 s
Frames( A4 g! G G, f1 P
Function rings. ?0 H% l& y( o* ^$ M; w5 C8 Z
G-sets" N2 C( F7 e& o
Generalized BL-algebras I; Q9 z4 J o+ C; w E
Generalized Boolean algebras
: D9 ?' E) c5 s9 iGeneralized MV-algebras
; f1 K- s4 X0 u s0 UGoedel algebras8 I- J% Q3 {* k4 p2 U2 P/ z
Graphs
9 @( F2 n% T" ~Groupoids
; ]) q3 M Z) B; lGroups
/ i) P6 i4 u. J3 vHausdorff spaces8 {- E( T, {5 e( h! G
Heyting algebras
% `: f! c% O* vHilbert algebras* V# |3 i; L) U8 ?" G0 G* X
Hilbert spaces
. r4 t# w4 K! z' Q# KHoops5 v9 E0 z# H3 K s
Idempotent semirings
6 g( r7 O- U: p1 q" Y0 ^Idempotent semirings with identity
. p B( x$ m9 ?2 g6 P- yIdempotent semirings with identity and zero0 n% r- j: ]. V- _9 I/ V0 ~
Idempotent semirings with zero4 P, E* y5 F+ C5 b( X! |
Implication algebras
) F9 U- J3 L' B* q( jImplicative lattices
3 k: g0 n/ R8 h! q8 b SIntegral domains
0 U+ I0 ]0 Y! JIntegral ordered monoids, finite integral ordered monoids3 L% K0 s' z9 M# r( y
Integral relation algebras
- I% l. Q3 R, v+ n3 Y1 yIntegral residuated lattices2 @; s6 G: d o
Intuitionistic linear logic algebras: }; K: W1 c2 v' ~, n
Inverse semigroups
2 C# U+ V. p+ R- RInvolutive lattices. M8 u, l8 R" A. W
Involutive residuated lattices
* D z; x L3 u- k bJoin-semidistributive lattices
! @4 A/ E: b# X2 w' Z2 D/ a6 LJoin-semilattices! y2 B$ e" J) v2 A, j
Jordan algebras
' ]1 [0 u! V/ n: U# c* q! t' `Kleene algebras; T0 K4 B- c7 M0 q# Z& c
Kleene lattices2 g: g( W6 b( [* k
Lambek algebras
6 @ p* y( X8 y% A7 R8 O1 HLattice-ordered groups3 f5 Q- _2 o- Q% N8 j, F
Lattice-ordered monoids
1 x: @5 m" f8 @+ ~Lattice-ordered rings! L4 [* W! E* ^8 ]
Lattice-ordered semigroups
' Q& G( e- b; K3 U9 T( Z2 s2 A) Y7 pLattices+ u6 [) [7 U" P' D- @% \
Left cancellative semigroups
5 B" V, W4 P) Z9 Y8 w6 \$ _Lie algebras4 y* H& K# R$ B
Linear Heyting algebras
/ s& ~6 p" L# t: `9 HLinear logic algebras9 y' C a' M1 W. g/ G/ r; Q
Linear orders
8 O' f; ]$ q5 V, ~4 t# M! ?( W2 aLocales
; ]4 y7 y, f5 T" j wLocally compact topological spaces
4 ^7 B3 ]( [. T& ?8 Q1 _: c% M, PLoops8 ?9 g) m3 A( G3 ]- I& E
Lukasiewicz algebras of order n
1 L3 }' L- n6 k/ EM-sets7 s. A, G z$ w2 {
Medial groupoids
% u U }2 C$ nMedial quasigroups- T* S$ S# P" J5 i: c7 k( z
Meet-semidistributive lattices! m C$ n4 m+ k1 l9 q
Meet-semilattices( ?7 p, B8 P" x' [
Metric spaces3 J2 Y8 X/ Y3 ]' S5 V9 y; L
Modal algebras( l9 `( ^' g( M' ?; t0 D1 P' M# N
Modular lattices
2 d r- s" X& l: UModular ortholattices8 @/ w% e# ]' F V: T% G9 _
Modules over a ring
8 C# a1 c2 J6 |; D* a$ v0 FMonadic algebras
+ @2 V7 c. r5 l0 u% }Monoidal t-norm logic algebras1 z4 p$ N3 Y8 B* U7 B8 t9 K
Monoids, Finite monoids, with zero
3 T% ]' K2 i5 k2 u9 T" L7 dMoufang loops9 w) }; o1 k: }! Q1 R6 S
Moufang quasigroups
+ Q- U, m2 S+ k3 hMultiplicative additive linear logic algebras6 }, M( K! J: f) T0 y$ e
Multiplicative lattices
1 s, G+ _/ A( m7 L$ x5 y/ l7 wMultiplicative semilattices$ W! c- K- T4 ?6 O; R- K; u
Multisets
! k: O+ v' u" C& LMV-algebras
: z! R' H6 v( x! y% Z9 hNeardistributive lattices
7 U O1 f d7 f$ kNear-rings
2 @4 w. f0 m7 Z* hNear-rings with identity* r2 d& V' o9 g1 Q
Near-fields
1 N* y1 n+ K, H2 I4 LNilpotent groups+ d$ N8 c' Y) _% c }4 ]
Nonassociative relation algebras% J& W* ^3 X+ B8 z; E8 l
Nonassociative algebras
( I+ [% R) |; l! vNormal bands
) z8 r `& n4 G- n0 Y+ x$ |Normal valued lattice-ordered groups
- V& e' f# q7 B% C# A! @Normed vector spaces
+ {1 c1 {1 j8 i; C, [- g, sOckham algebras
: e. e, M- f0 `( j6 t' ROrder algebras/ ^4 _1 A& I a1 z# ]9 t4 M
Ordered abelian groups
O+ t/ d/ V7 z$ d( E1 {Ordered fields( {. k _' d- V) c/ P
Ordered groups
% m7 r5 ]7 s2 O0 J$ _1 F9 O/ eOrdered monoids
( c/ J, L4 Q7 P& [; ?: a* Q# ROrdered monoids with zero' H% \6 e% K% {2 h) Q- ~/ P+ V
Ordered rings$ x/ D5 j* ^' z8 H2 t/ o1 J
Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero
+ X, r# }6 z/ H1 u/ WOrdered semilattices, Finite ordered semilattices
1 I8 X" r/ U- J2 g5 T+ c5 u; o3 lOrdered sets
- a. h! y) H5 D2 LOre domains5 E; T# {3 `: s+ c; a8 }/ d1 R
Ortholattices
0 ^) H3 r) x0 |' |0 {Orthomodular lattices0 j8 D& u$ R& ]4 Y" o
p-groups& i! O8 S8 c9 f! L
Partial groupoids( l' [( V6 I) W6 ?) p
Partial semigroups% J( f6 G# x9 j X. y+ O
Partially ordered groups
& ?- p2 Y( }+ K, mPartially ordered monoids
4 e: a- f& Z( tPartially ordered semigroups/ s& X3 S9 W$ p+ J: V
Partially ordered sets( ^8 h" V- T% T: M/ u5 Y( V6 E0 |
Peirce algebras4 V- a. C; c4 ?) T' ~" x
Pocrims
* m) g% M, t8 [& _1 {" @7 ^Pointed residuated lattices& p+ H% l. z; k
Polrims8 i) @ T! j& x6 F7 Y
Polyadic algebras
. j. r- N) Q) L/ U' m& d5 E+ @Posets) `3 q V1 ` ]1 l# O+ A' W" ?
Post algebras3 m. S+ x; J0 f; V6 R( S2 d
Preordered sets
% s% k2 i1 L' x/ x1 C5 zPriestley spaces
# m3 A: [. F: T- D2 _) ^/ x+ jPrincipal Ideal Domains3 W' p* z5 G) O M' @/ {
Process algebras
8 ^( d) y. e& Z/ F' n) `% d9 FPseudo basic logic algebras W( M! V+ }1 L3 N/ L8 _, _3 d( W- T
Pseudo MTL-algebras) w6 Q- y1 L- t, B0 k0 n
Pseudo MV-algebras. F- _# N( c' p1 I
Pseudocomplemented distributive lattices* y9 s$ B1 f- T5 V2 [
Pure discriminator algebras
% b; A7 |) R& l0 u. FQuantales/ G! A( }' Q4 P, l# n( r1 z
Quasigroups5 D: @6 |; N1 K- K3 @& \/ a
Quasi-implication algebras
) X5 ~2 V0 P Z- [) N* w# d2 W2 B* wQuasi-MV-algebra _& S. q+ c: ~- y, L* \( V3 d) I
Quasi-ordered sets
6 @" `, C! r- \* f# n4 CQuasitrivial groupoids
3 m" V* o% j# p2 |' ?/ uRectangular bands+ k$ X7 b7 R. T5 W H
Reflexive relations
- f) A5 k- h# n3 W, O$ BRegular rings
+ X7 P, ^$ v L* f- sRegular semigroups2 B, X6 c/ r# @3 J
Relation algebras1 ~; w: j6 L" c- W i- G2 B
Relative Stone algebras
. S( S4 N$ s# |* ?, i3 s* ?) k! DRelativized relation algebras
2 D& {9 s. R T! A. lRepresentable cylindric algebras
" O$ y4 X; U. @4 rRepresentable lattice-ordered groups G9 j7 }2 b- }
Representable relation algebras
/ Z6 d4 b2 ?- s& m# WRepresentable residuated lattices6 h! v1 b) T1 [5 H$ [' l
Residuated idempotent semirings; N7 J/ C. I s2 r
Residuated lattice-ordered semigroups7 c) E3 F) S4 ?( b- k. T) @
Residuated lattices* e3 ~" Z) z5 V, c% [0 ~$ Z
Residuated partially ordered monoids3 m' L7 L: M' U
Residuated partially ordered semigroups- f0 d% r3 n( y" G
Rings; V+ Y; M9 {4 ~: w5 Y( H% a
Rings with identity! X& e) U$ [6 X2 }
Schroeder categories
( |0 T {% [. l! E8 T% @Semiassociative relation algebras5 s% F) t- x' v4 l
Semidistributive lattices! @4 [7 M* ?( ?4 D4 S
Semigroups, Finite semigroups
. Y y+ R0 R- q- ]! ?4 _Semigroups with identity3 r+ {- e0 s' k& T4 m; W% [9 J3 t
Semigroups with zero, Finite semigroups with zero
/ H* \- t$ d% j2 ^# d. {Semilattices, Finite semilattices
, l- D" v9 M& ~3 fSemilattices with identity, Finite semilattices with identity
4 e v8 B5 z; h1 i# d7 x' SSemilattices with zero
; [1 F+ f1 Q/ ~8 @1 PSemirings
9 s' V, T& f& zSemirings with identity
3 u5 X& d8 p& F# r; q; @Semirings with identity and zero
0 s; \5 ?( z$ g3 |) G' o xSemirings with zero
5 ?* K4 l7 X. m T* D- LSequential algebras8 i& ~2 a. X" z3 u: I# f; K9 W
Sets, F- D% H8 [) g, k) K% a& h7 @
Shells7 |- X$ `' x" \2 M" e# e( V/ C
Skew-fields: F% Y9 e+ a: M z& h
Skew_lattices
# `3 Q" |5 G ~/ n5 s- r9 a. jSmall categories
/ i+ w+ \: J8 v1 O& SSober T0-spaces( D* {2 ~: S9 |# q' n* U
Solvable groups& a, U" U! m" O8 Q7 P3 z
Sqrt-quasi-MV-algebras: f" c! S3 o- [" x6 y* F+ S5 M4 R
Stably compact spaces/ i5 K0 X, X$ B2 d" Z
Steiner quasigroups4 I8 w! K1 N/ \1 E
Stone algebras( y: X6 n; f* P2 f
Symmetric relations- }/ n2 Y4 L( k; o
T0-spaces
6 J+ X: h7 k) o% T, _# {; PT1-spaces3 T* V4 ^8 f3 g+ v. f! d
T2-spaces/ ]* {/ i( T$ z y/ K
Tarski algebras
) Y: o! ~: b, l/ i, Z& aTense algebras. x: E4 g3 u5 |1 u$ h2 I
Temporal algebras
) n3 q! P/ q, K" b4 [Topological groups
% ~! a* H7 l" D+ k4 C4 ^3 q; X8 m( `Topological spaces& V5 s; D2 t- X! P' h
Topological vector spaces
5 [ `$ n( ?! zTorsion groups
: l" T( R x9 s% S- lTotally ordered abelian groups( Z3 q: |) k$ g! J
Totally ordered groups; b- ] n0 f- f
Totally ordered monoids9 A! |2 G- N9 N. q4 X0 q! u
Transitive relations, w" R a6 k' q( i, u1 E% m9 u
Trees; [, o, p: ?# q5 x2 F! y+ R2 R
Tournaments+ T' V" ]4 s, \2 r
Unary algebras! s! }! y1 Y U- f3 A
Unique factorization domains
2 _. ~: x. g2 A x8 t. b% gUnital rings4 f0 T6 }0 C' x/ f* [
Vector spaces: ~. G4 L# Z9 Z
Wajsberg algebras4 K0 z K7 l4 B* P& r8 q* S
Wajsberg hoops
, N. c8 q7 k& S6 P' ZWeakly associative lattices
* P: B- `5 i" M* A3 p: dWeakly associative relation algebras
) J6 c; w9 R/ T# e$ d! r0 KWeakly representable relation algebras& T9 g; I' V2 b6 m% v6 ]9 M
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