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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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+ H6 g/ X; N5 X+ L+ H5 H* h" ]6 U# l
" T' `' K p1 D, J a
Abelian groups Abelian group& X, B0 J6 f' F3 m
Abelian lattice-ordered groups4 _5 n9 Q' w, m) O7 x
Abelian ordered groups8 O, O4 R3 q2 n3 Z6 |+ M) F3 W, b3 V
Abelian p-groups
) s! ^9 v) u9 G' z- t) rAbelian partially ordered groups
! c! [% L& L5 W/ ]; }3 qAction algebras Action algebra
8 _. X/ w; _4 a' }Action lattices
+ R) B' l, {+ V+ o) `Algebraic lattices3 C/ P7 E! O9 }5 ^0 f
Algebraic posets Algebraic poset
3 L& e" M3 j p: |4 S6 aAlgebraic semilattices
{' p; J3 M2 G+ N4 EAllegories Allegory (category theory)( x) h* Q$ i; z6 N
Almost distributive lattices, v7 ~3 T7 {4 N+ W, M. f- j5 a
Associative algebras Associative algebra
- f6 Q: f5 _8 OBanach spaces Banach space
" H8 U/ [- B/ F8 ]' VBands Band (mathematics), Finite bands4 j0 J/ S% D/ f2 J f
Basic logic algebras
+ B3 U/ L2 c1 K6 s8 _BCI-algebras BCI algebra' j, \& v$ r- Q0 y2 q
BCK-algebras BCK algebra
8 q. t+ o* t0 t7 I/ @BCK-join-semilattices/ Y3 B" X) Q+ c6 w" @ X$ E
BCK-lattices. i6 i5 U+ I* V- |- Y7 D! b2 Z
BCK-meet-semilattices
- D- a- F0 W$ }' X1 X" m5 I9 hBilinear algebras
5 u) Q/ ?, t5 a, A+ XBL-algebras
/ P0 D9 c6 Y$ I! `+ n3 A4 iBinars, Finite binars, with identity, with zero, with identity and zero,
0 s9 D- c3 P6 n& C7 E2 _# }Boolean algebras Boolean algebra (structure)
2 S! x5 U- U8 k4 `Boolean algebras with operators
+ Q- B2 Y# V6 t, X9 yBoolean groups7 ~5 w. Y! K1 c" E
Boolean lattices
: W& r& `; l; W. K9 rBoolean modules over a relation algebra" {7 L$ |+ `9 v
Boolean monoids3 j* Z, R8 w9 ~9 U# h8 ~4 W6 \# x+ F
Boolean rings
. `7 p9 k0 a! x9 Z6 L/ P3 QBoolean semigroups
& x h2 o6 C: s4 SBoolean semilattices
6 M, X! m. }6 _& n4 p# [Boolean spaces/ p" s+ t; T: R
Bounded distributive lattices, ~3 N s$ E- Y7 s# C: L p
Bounded lattices
( q. E2 m; B7 K- j ^Bounded residuated lattices
3 d# x0 R/ q* N$ f* P: I; VBrouwerian algebras
! P$ N% T1 |+ I; t/ d5 H8 mBrouwerian semilattices( Q( e: a: T; N; x$ V; ~( b; {
C*-algebras5 p: r1 F% ? ^# n
Cancellative commutative monoids
, K4 ~8 e* i2 D y$ Q& [Cancellative commutative semigroups
+ O% `. n6 r4 _% ^/ |Cancellative monoids C; l4 z! t u3 V1 o2 D2 Z
Cancellative semigroups2 s& y) G3 S! F# v0 x- o
Cancellative residuated lattices0 F8 t2 v' w. F
Categories) S" ]! Y' |, K+ j* G3 h
Chains
3 P- k3 u Z/ \# aClifford semigroups
( R& i K. q# W2 \9 L6 x6 @) xClifford algebras' W. [: v" G" {" L' ]7 j" E
Closure algebras6 x' a5 k) T1 I
Commutative BCK-algebras: p2 y# B; C. ~- h
Commutative binars, Finite commutative binars, with identity, with zero, with identity and zero
$ _9 t! C% P0 S* E2 R" Y6 ocommutative integral ordered monoids, finite commutative integral ordered monoids3 u1 _' s& w4 b8 H, B" L- p+ l
Commutative inverse semigroups
% E) C; R( ]# s: a- MCommutative lattice-ordered monoids; }9 @' `7 z+ B) W# G7 X" A
Commutative lattice-ordered rings
( o4 V7 W0 c. i% gCommutative lattice-ordered semigroups
7 g" h$ c( n2 xCommutative monoids, Finite commutative monoids, Finite commutative monoids with zero" x" g, X6 y2 d, W5 o
Commutative ordered monoids
. ~. U0 y* g- N2 SCommutative ordered rings
; F: ?: Z# Y6 e5 B: ^Commutative ordered semigroups, Finite commutative ordered semigroups
' ?5 M% ^2 {% c# dCommutative partially ordered monoids
4 L- a. t& Z, V- s" |Commutative partially ordered semigroups
/ g; N6 D( v1 {& @/ u- j! N* ?Commutative regular rings
% [0 L) j) j. d ^6 P; ?# xCommutative residuated lattice-ordered semigroups
$ B$ ^ W9 }% Q9 D4 uCommutative residuated lattices' d W, X0 ?7 } f E% I
Commutative residuated partially ordered monoids
0 {, l& N1 d/ `: M, b" _Commutative residuated partially ordered semigroups
6 K9 c' @* R0 I7 H: J, SCommutative rings
( \7 F b Y5 N. K9 q: lCommutative rings with identity- Z4 D$ c" u8 p" c' X
Commutative semigroups, Finite commutative semigroups, with zero
/ w5 ]! V |8 a- DCompact topological spaces
- D f) H l, q# l+ ]% ^7 Q9 `/ u8 qCompact zero-dimensional Hausdorff spaces# }& ?" u" U8 G. b
Complemented lattices7 K. Y% F2 W3 H* W6 k8 L" ^7 P
Complemented distributive lattices6 B- Y. C+ ^9 s$ r
Complemented modular lattices
% p; o8 ?& |/ PComplete distributive lattices
* d- Y8 e! X r5 uComplete lattices
& Q# \$ R+ R# p9 K9 h+ W, mComplete semilattices
4 _8 I: X" K! a& X2 {* P7 W/ y5 `Complete partial orders) S( C( a5 O5 n* s+ l1 \
Completely regular Hausdorff spaces( f- ^6 s# O" V0 _ j
Completely regular semigroups
9 c/ p: V9 [) J& nContinuous lattices2 X) B4 ?. @" _$ j
Continuous posets4 N) @8 W7 Y' E0 B
Cylindric algebras
3 y2 l1 s+ K* z, CDe Morgan algebras
j# g4 O- _ V1 B. {& hDe Morgan monoids/ s4 y. u$ \: C1 _8 p* e
Dedekind categories
4 E! h& C) a/ a4 D2 d* hDedekind domains) U5 r2 {: V0 i# W
Dense linear orders: M- z# \ b0 Y( Y4 g1 n
Digraph algebras: M# ]9 b g9 p) ~8 v
Directed complete partial orders V& r4 \8 m* F( U* B
Directed partial orders. K. S/ P4 M, B6 {6 M4 [, s1 v
Directed graphs
* Z3 C$ W; m8 V. @ _Directoids" b3 C; p/ @6 O; L& o$ Q
Distributive allegories( T8 _0 H9 {( t# T2 ^; W! H8 V
Distributive double p-algebras
, c; U* v+ ~, u- Z' Y& s. g3 cDistributive dual p-algebras
+ ^4 R8 L s9 q6 J. oDistributive lattice expansions
8 B: d7 a- W( H! a! x0 JDistributive lattices
2 |* |+ H' ]+ A/ a2 TDistributive lattices with operators
, E. [# r6 U( E. RDistributive lattice ordered semigroups8 ^2 @' ?; C+ X# u: C
Distributive p-algebras
. K9 k, Q7 _# ]. Y; CDistributive residuated lattices! r! p) T; J7 V ^6 m8 C
Division algebras
: Y( `! d; o: [& HDivision rings
5 t+ I. b/ x3 R- C' d( e. C' J/ ZDouble Stone algebras. L7 F3 y3 _$ T+ b. M! a S& _
Dunn monoids
# r/ T9 y* M' H6 d- QDynamic algebras2 J+ u: o K; q; w2 I+ h" Y# p/ ?
Entropic groupoids9 R: l7 o' N4 T7 J& Q
Equivalence algebras
! c- y; `: p6 \& z& ~$ |2 SEquivalence relations
; a! C5 N0 Y' G+ \/ }Euclidean domains
- j7 C9 X6 x" K' H' y) G( yf-rings
/ i* y( a1 H) k& |( D2 f( M1 rFields
& g* y2 {# N$ s6 \, ?FL-algebras7 R7 g9 G1 h" @7 ?0 @
FLc-algebras3 u- A/ \0 V# w, R7 G. k7 U" O
FLe-algebras9 H& o8 k; J4 `; C8 c
FLew-algebras
( m& D' w; g+ R6 E. p0 E% G |7 ~FLw-algebras, t8 D) o& W3 {: Z$ H
Frames6 I6 U" s+ q |/ L# |
Function rings
' H0 l! I" S" f. {G-sets
' g& t8 R8 o4 s$ X4 UGeneralized BL-algebras! w7 K5 D1 y7 T2 L% @, F2 y9 l
Generalized Boolean algebras
1 O4 L4 I3 s, c1 aGeneralized MV-algebras
# S! R {6 @- n+ d+ c ~Goedel algebras, K( Z/ p( e/ m5 U$ ]& y
Graphs
5 F+ s6 k n' Q' \# J4 ]Groupoids
+ I& l: h0 Q) u7 i4 n qGroups, X1 d& a; t H. V# Y* U* I, d. ?4 {
Hausdorff spaces c t* E; [: w, Z. ]
Heyting algebras4 ?+ Q1 ?; ]1 T; @' c1 M
Hilbert algebras; [6 S: o! z- U- P/ o6 o9 ?
Hilbert spaces
. R* ~& q+ u8 H8 f% UHoops! P; b- x& U. E# C9 ~: M2 \$ R1 N
Idempotent semirings4 E0 B( m. u8 v X2 P, C, a
Idempotent semirings with identity+ G4 K3 h; P+ u+ o4 |! ^
Idempotent semirings with identity and zero
: H0 \& o3 s6 t9 r& I) Y, yIdempotent semirings with zero; H8 W: K3 N" d7 m W3 @
Implication algebras' f, J/ c7 {& y; X' y6 S+ @" r2 D
Implicative lattices9 a. M$ W F0 l* v; r
Integral domains
; h Y" X: t" UIntegral ordered monoids, finite integral ordered monoids- _3 z) \! w- Y, P
Integral relation algebras3 }; P" t! |# Z0 K: s( Q
Integral residuated lattices8 e( e5 e& t- j5 ?, I& T
Intuitionistic linear logic algebras
& ^+ H7 w4 @" T8 HInverse semigroups
$ R. o) O; X2 C3 Q( r7 VInvolutive lattices
, L) @( C( w7 e& D3 q, OInvolutive residuated lattices
. v# e" w# B( |) \+ `0 hJoin-semidistributive lattices$ I* \/ x4 k7 X5 }% ?0 o
Join-semilattices W/ n1 ]( |8 a3 E4 z+ m
Jordan algebras
$ ?: i' t5 o+ l! ^8 b8 AKleene algebras
# b' [* \; F# V% h: `( x0 p% ]" ]Kleene lattices4 S1 s" ^: B% d6 V( x
Lambek algebras
w v& m4 v4 ^; hLattice-ordered groups" H9 `3 g4 X) _! Z: N2 B
Lattice-ordered monoids* c- E( V& J: W# A( u+ z
Lattice-ordered rings: v; q" d3 ]* W
Lattice-ordered semigroups
- U3 m8 B, V0 XLattices
. T0 @" a/ a: m. BLeft cancellative semigroups
) Q# E: S% s% x1 m4 k# LLie algebras
+ E1 y. Z9 e+ B" W$ ?5 }/ SLinear Heyting algebras, ~0 n9 y( w6 B4 W( g
Linear logic algebras, `& F( o% t6 V6 [! j/ j
Linear orders& B3 [0 p8 z4 Y
Locales
- A4 P, V" f) R2 K. x9 u1 f$ gLocally compact topological spaces
+ U3 T" B- i5 B- Q1 r! ~/ OLoops
& G2 w, n" A6 y2 cLukasiewicz algebras of order n
! D0 Z3 u% i/ @, k# @. \ uM-sets
' b4 M; Y/ V' G* }1 ~% N/ yMedial groupoids& Y m8 L+ t2 C2 R# d
Medial quasigroups
( |6 g3 s' k" K$ w/ |Meet-semidistributive lattices [- I4 J2 E+ E9 S- j
Meet-semilattices
: Q, q+ P: n! ?& n* }- B% I7 fMetric spaces
' } X3 r: N9 R: _, v, O1 G/ hModal algebras
# A4 U" F5 ~: s P" j) c1 MModular lattices" R9 X8 s& L: d: M6 E. B: i
Modular ortholattices
( b4 _* T: D" kModules over a ring
4 a5 Z9 J. Z$ M, F. r; HMonadic algebras
b% f( h; U. M6 L/ yMonoidal t-norm logic algebras
9 g0 j" b, n: i: s* MMonoids, Finite monoids, with zero# s3 H7 Z% ^8 O% ^# S2 M9 ~' \: E6 \
Moufang loops
+ J; F! b; X2 |Moufang quasigroups j5 q' ]/ O, ~" O" P
Multiplicative additive linear logic algebras+ F: N' c+ c0 C
Multiplicative lattices
- e; R* f) ^0 PMultiplicative semilattices
6 S, v" T: _ w- \5 XMultisets$ e! p/ p I2 k4 o* W8 @
MV-algebras
& Y7 d7 e4 M" MNeardistributive lattices$ Q0 P! v$ C7 i2 C9 A! |6 c
Near-rings( w* K3 o* D* f6 f2 m: F4 g9 ^
Near-rings with identity
9 ^- w0 C O W: w5 LNear-fields
3 n: [4 u* O4 ONilpotent groups
0 N( r' }% \7 c" i/ H' [9 hNonassociative relation algebras; B% Y" P- w/ k _+ r
Nonassociative algebras6 b9 z3 l0 m: ?# E2 o8 O
Normal bands
+ g1 F( C) w) q' g- u6 e INormal valued lattice-ordered groups
% Y5 W% Z0 x7 B: H8 DNormed vector spaces
+ z) v/ q6 ?; I- Z4 uOckham algebras
" S2 {! b- g& b9 D5 u6 H3 e! AOrder algebras" {8 k2 G0 V" X1 h0 W
Ordered abelian groups- N# e8 P* p A2 T3 K
Ordered fields
/ K X; I9 {8 Z/ i! a6 L$ U! k& MOrdered groups
* _1 s/ Z6 P8 @- _# w' ?+ L5 ZOrdered monoids
! x) P: W7 n, M# D& A8 T2 cOrdered monoids with zero
. t. a7 r3 T% k: c C+ A' t! COrdered rings. Y' R* b, k! Z9 a0 d+ _6 l
Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero
& P2 p7 p$ W6 E% LOrdered semilattices, Finite ordered semilattices2 g) \& r6 A0 i
Ordered sets
3 j1 _& S7 x( R' R1 hOre domains$ E7 |$ V" K: @- I# O/ e6 c
Ortholattices
; s! I' {7 U$ g w; tOrthomodular lattices" P8 @2 _& T" B" F" B
p-groups) E6 {& F& u2 Z# d8 T8 G
Partial groupoids1 m! P0 z7 i4 e. T& }/ z
Partial semigroups1 a. u' J; l' i0 B( f f! G' U: M
Partially ordered groups
5 c R8 b3 R w! SPartially ordered monoids
8 |6 |9 [. I7 }: GPartially ordered semigroups
0 W5 S1 j! z$ B9 l+ qPartially ordered sets
/ o& ^9 y; F2 E5 JPeirce algebras
4 l1 `5 K. ~" v0 s% DPocrims
7 m7 t1 X" ]3 K9 |. DPointed residuated lattices
2 V$ ^; \% H: h8 f p6 ~2 `( ?+ ePolrims& o9 C; a, X0 @
Polyadic algebras4 t3 k, w$ A) \
Posets3 T2 l% E! F5 T8 Y* i6 \0 K/ G
Post algebras! i. a0 Z) i" w7 o9 j
Preordered sets
; A1 O- h& s" l" l/ lPriestley spaces
% I# g& T9 e& NPrincipal Ideal Domains
8 ~, P: G$ v$ M8 n- ~7 u# kProcess algebras7 Y7 r) e) @5 N+ z; Y9 v$ Y: i
Pseudo basic logic algebras
9 M' D! w' W+ `% fPseudo MTL-algebras5 \1 p: W! ~- y" w
Pseudo MV-algebras
% T+ }, q; j# j) U8 X0 \4 S: lPseudocomplemented distributive lattices. K) X, E* [( g- q! c( X1 G5 C
Pure discriminator algebras
$ A( F# n |( N: C% ~Quantales, c: D t6 b# w& R
Quasigroups
& v; v3 \- p+ A, MQuasi-implication algebras9 E0 `& L$ p8 f4 z- o1 x
Quasi-MV-algebra; O |8 {7 }$ _! x- R; w' g
Quasi-ordered sets
1 Z; m5 f$ M0 z$ B) }1 eQuasitrivial groupoids1 u) Z3 Q5 F e( E: { v6 C0 C
Rectangular bands' u0 F5 [ `- t- A# f% Z9 M
Reflexive relations
+ _. T, d' r! ZRegular rings
0 U5 t- d8 ~6 g. C1 t' BRegular semigroups
" I+ \) P$ ^, F; ^# c8 SRelation algebras
- @1 P: ^4 Y5 a4 H) i9 jRelative Stone algebras* `& v1 c5 r0 X" R4 p
Relativized relation algebras
, @. l5 O# L1 J8 d& m* M2 w1 dRepresentable cylindric algebras
# L( X8 \# U2 n. W* q2 NRepresentable lattice-ordered groups
, z- z: Q8 C5 hRepresentable relation algebras
, A& E! \$ `% W& L- Z& b5 w& DRepresentable residuated lattices8 V; ~1 p7 f2 O3 i2 W2 j
Residuated idempotent semirings
) ?( s& z/ h8 h L( z4 BResiduated lattice-ordered semigroups# v6 C9 }& {7 `+ ~; Z. q" q4 i3 D
Residuated lattices
5 B6 _( Y7 [$ j; u2 lResiduated partially ordered monoids
7 Z) T1 a8 T$ H5 @ D. p7 J) `; UResiduated partially ordered semigroups1 D, P' v6 l" f
Rings0 G/ l! b: a/ j0 c, C1 p* w. _
Rings with identity
7 h% j. ?4 h) r) rSchroeder categories* u- f- X8 n) X/ i4 H
Semiassociative relation algebras
" z% `# m/ N5 YSemidistributive lattices
i0 H P) B& y$ z& ~Semigroups, Finite semigroups! A2 V4 X0 v+ q& ^; K" D- K
Semigroups with identity3 k, \( C. q, s. v5 s% T) y
Semigroups with zero, Finite semigroups with zero
" F4 F2 V3 P& w3 {7 n7 SSemilattices, Finite semilattices2 a$ l; R- Y |9 r
Semilattices with identity, Finite semilattices with identity
j- n% y# Y+ Z" ?& n" oSemilattices with zero3 i! N0 r; Q1 H2 i
Semirings- a+ x9 m+ x5 X$ G: W0 t/ r" k+ q/ f
Semirings with identity( _% y3 x, a8 T& k% ]
Semirings with identity and zero
* {9 w j9 W$ [7 P7 B5 e0 JSemirings with zero+ U- Q9 G3 M. G# @+ Z
Sequential algebras1 l, j: `+ g. b. k/ X5 R, N
Sets
# a' _$ [5 e( M7 U5 |Shells0 I* s" p( ?3 ^" @/ F/ T& k
Skew-fields
5 h" I1 I7 v/ c) W# ?Skew_lattices
" E5 g' R$ K) sSmall categories
y5 a" W/ b5 U+ \Sober T0-spaces
: R; z, e. U" r( {, L7 P/ {Solvable groups- J/ |( i3 `1 m) j
Sqrt-quasi-MV-algebras8 l/ R" ^7 S- D$ C
Stably compact spaces/ w1 X6 f6 ?+ B: D+ B9 ]7 I
Steiner quasigroups
9 }; y/ t5 b4 A V$ W: J* gStone algebras
7 y2 _3 h8 g$ H4 {2 G) @+ nSymmetric relations
1 y5 h" J6 O5 d" cT0-spaces
; T4 U' T( o) R+ T7 K$ OT1-spaces
0 a+ P3 t' ]2 P$ Q) q$ w; VT2-spaces
; k) Q; | x, X7 [' p iTarski algebras: F+ h9 r! o! A8 w3 I
Tense algebras
3 S3 I* K3 R7 a& ], }. m& F% z, cTemporal algebras- D. |3 `3 i# M9 R
Topological groups/ `# h3 `) Z( n1 w& t
Topological spaces
- F4 [& V I# Q% h& I) k9 GTopological vector spaces, F8 W! G" n/ Q& C/ l8 f
Torsion groups
. j% M4 k6 ~# ]. ]! BTotally ordered abelian groups
& h! D" o2 M S2 l3 {Totally ordered groups" m# g- H* z- c7 {6 \) m0 b" k
Totally ordered monoids5 E; Y% H3 |4 K& C
Transitive relations
6 L# J& f- R/ c8 G+ q- STrees
, m8 O% w7 {1 @1 \! \" w( YTournaments9 G8 _ G! H' A
Unary algebras
) u6 G4 Q8 Z$ o8 }) PUnique factorization domains
+ s# w+ Z G+ E: O- yUnital rings U2 P; [8 }3 L
Vector spaces, o6 y* O1 _% K, B4 I$ [
Wajsberg algebras4 f( r# `) d) L0 N' Y
Wajsberg hoops
2 s) f) j# f5 e" @* G1 {Weakly associative lattices2 h8 w1 h/ M, M& l: T) x
Weakly associative relation algebras
7 U+ V" x Z+ h4 q! a' H/ f m# MWeakly representable relation algebras
4 W; r: }+ T9 ~3 ^! H& I |
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