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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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G1 F; o4 f& N
C8 P8 |! L% A# M, @Abelian groups Abelian group% c: Y& |' ?, C8 C
Abelian lattice-ordered groups, Z* @( t$ N: y7 U( p/ h
Abelian ordered groups3 w6 Z* N+ `5 H0 O
Abelian p-groups
9 H1 I/ s. G8 C2 T' AAbelian partially ordered groups
. V" J) A5 [* A# K: {$ N1 T: j% ^5 |Action algebras Action algebra T% Z& R; P/ l+ m
Action lattices- M7 z9 n0 F$ ^/ }5 z3 q
Algebraic lattices
3 Z8 j- {7 K4 k4 H4 h6 wAlgebraic posets Algebraic poset
/ H5 x* d$ m6 mAlgebraic semilattices
8 j) |+ d) |* J6 Z! I( Z- _ XAllegories Allegory (category theory)
7 @5 p) E- H/ d. bAlmost distributive lattices
# P) [, U- Y; [: M0 c! |Associative algebras Associative algebra
. v8 H( p( H. i6 C0 } lBanach spaces Banach space
9 Y3 Y# L4 S$ r8 F- ]Bands Band (mathematics), Finite bands
) a% ^9 ^, L0 i5 ]. |! O3 yBasic logic algebras
0 B8 m4 @* X1 i2 p# F3 O4 l) zBCI-algebras BCI algebra
V% d1 n+ E. n" [BCK-algebras BCK algebra
% d- e# }* ?8 M" \! B) |0 k3 G6 BBCK-join-semilattices2 W! o( d) j( w* Z* E3 {
BCK-lattices$ {6 A2 e* w4 H0 k( B
BCK-meet-semilattices
. Y6 [3 n% k% v2 X( w; Z$ ^* ]9 `- jBilinear algebras
# D. p3 i6 w) ]BL-algebras7 E+ \4 w$ i* c
Binars, Finite binars, with identity, with zero, with identity and zero, 5 q6 a7 R& ]; D
Boolean algebras Boolean algebra (structure), P" Q& U- Q# |3 M
Boolean algebras with operators
2 _/ v' i: K/ J, a, ]Boolean groups
9 b: F3 g/ A# O8 V4 U/ MBoolean lattices. {5 t1 W" i! [. y8 F+ C
Boolean modules over a relation algebra
2 O$ I( a8 z. k) h4 Y9 A- ?: CBoolean monoids j. y5 W5 ]; t0 u
Boolean rings9 ]9 m8 r* ?9 ]* z
Boolean semigroups0 ?! ~! Y. k" J* y5 g1 a
Boolean semilattices
) g' P5 e" W9 G1 i1 J4 r B6 _$ [% kBoolean spaces+ N+ s j3 T8 s. d/ j! h
Bounded distributive lattices
. R f' C7 @0 p; I$ C1 i5 D% eBounded lattices5 I; Y) _% L0 B" h3 `3 R
Bounded residuated lattices
h9 E' U' h# L- N$ ]( cBrouwerian algebras
4 e* g4 k, |4 Q5 O' GBrouwerian semilattices
b& K/ U" d; ^5 f9 @- R6 HC*-algebras
5 T2 {3 D4 j, k# iCancellative commutative monoids
+ M& u* C$ U) Q0 H+ p3 ^Cancellative commutative semigroups
; [5 U: [" s. o' P# M8 ~4 l8 OCancellative monoids7 U/ T' Z/ D# O& R
Cancellative semigroups
* o7 s. M4 A5 F! k* p) `Cancellative residuated lattices& X7 w/ o: w. W! x K
Categories$ W0 m, @! a/ f; j9 D! C4 g# G0 }
Chains
0 v0 P4 J/ N- g4 z: o& [Clifford semigroups
+ F+ Q4 P' G' i7 {, BClifford algebras0 m% q2 N |! |: l
Closure algebras
" x6 _5 E9 @9 Q5 O, M+ h* UCommutative BCK-algebras
* ?7 p E4 Q8 s) \1 I7 S' ~% qCommutative binars, Finite commutative binars, with identity, with zero, with identity and zero ( q& C& x. v+ }. K* d x' r/ h |
commutative integral ordered monoids, finite commutative integral ordered monoids6 f$ [/ a& M' ]8 q8 C& Y/ E
Commutative inverse semigroups! @+ |. V2 K$ ^& q/ ~
Commutative lattice-ordered monoids
( s8 P, R9 p7 G+ |6 r* ]8 T7 FCommutative lattice-ordered rings
- R, c6 @& A! F# U' HCommutative lattice-ordered semigroups$ H) }; I0 @, ~0 E/ _" _3 s
Commutative monoids, Finite commutative monoids, Finite commutative monoids with zero6 G3 s* o M1 r- {
Commutative ordered monoids
0 {! C: i8 a, J- LCommutative ordered rings# {0 r" R' m7 ]; L* n
Commutative ordered semigroups, Finite commutative ordered semigroups
1 |. Y- N3 H) N! ]6 |Commutative partially ordered monoids4 V9 x. J. m: g/ g' O) t- f
Commutative partially ordered semigroups
3 ~8 g% ?* j/ D6 UCommutative regular rings( s1 y+ j$ u0 k( U) n4 _( A9 M# C
Commutative residuated lattice-ordered semigroups' C- U0 f2 o- Q9 K9 e! U0 B, z
Commutative residuated lattices
' s/ O c! a2 h9 ?8 f, r8 s+ v% gCommutative residuated partially ordered monoids" o+ j% t2 D* A" v1 q& K
Commutative residuated partially ordered semigroups
+ f F$ U( y7 O. {; B5 V# }- LCommutative rings3 `$ e: s' \1 d$ h! d o# X) G3 b' Y' M. y
Commutative rings with identity0 x5 U' T/ M$ r6 m5 z; Y- `+ ]9 M
Commutative semigroups, Finite commutative semigroups, with zero5 R* B/ K% L d' e, C
Compact topological spaces
& I( W2 p) N+ ~: Z! {. A$ G* ZCompact zero-dimensional Hausdorff spaces: P# K6 ?. q9 ^" Y7 U% w3 P( [
Complemented lattices
, n+ j- b+ x( ^' t" w) `$ C) JComplemented distributive lattices9 m9 m l" V( F: C
Complemented modular lattices
- H2 F6 M; c" H; c" [Complete distributive lattices
- o3 Z7 v! K% y2 s& ?) eComplete lattices% \6 d% z1 y" A0 \2 F) |7 o3 o
Complete semilattices
" N9 i& j& {" ZComplete partial orders
' h0 g0 Y* D& o: f& {Completely regular Hausdorff spaces) \, P+ ?# Q3 w/ t* i# A9 P
Completely regular semigroups
8 d5 ], t/ z: y/ j5 q' XContinuous lattices4 @1 T4 y1 e" x6 [
Continuous posets
- _; K; s3 i0 c8 SCylindric algebras
! K( i# |1 u9 V* g* |1 W) r+ dDe Morgan algebras3 n2 L, l1 c* a$ p+ X/ f c
De Morgan monoids& z* W4 b! j( _+ w. Q* w3 `
Dedekind categories& }, o( U4 k9 O- L! L% Q/ S
Dedekind domains
, [$ ]* X) O; CDense linear orders
, Z3 ~: @0 s/ O* k3 j5 E1 zDigraph algebras8 a$ j# m) C; [6 }( H
Directed complete partial orders
4 x' Z( Z7 W S0 ~- J, F1 jDirected partial orders2 Q- J! D/ e5 @- t
Directed graphs
+ n/ h$ i6 \$ }! o0 {* Y+ N: @* KDirectoids7 o4 q! v$ d& ?$ _% O, T
Distributive allegories
" Q( y- Z' V9 n# B2 K1 yDistributive double p-algebras
( S- ^2 q3 m3 FDistributive dual p-algebras5 V, Q9 m- N4 p6 V; }
Distributive lattice expansions" y; b: i/ }8 N/ H; t/ \: h
Distributive lattices
( Q N: d3 @, A$ y5 ?0 _$ I1 dDistributive lattices with operators
0 y" X* w1 _2 X0 A" VDistributive lattice ordered semigroups" U; h- y' z4 T0 V! H" I
Distributive p-algebras& K; t, A" h: l8 [9 f9 z8 ]' g
Distributive residuated lattices- c2 e0 [4 q: e8 v
Division algebras3 G" b: W7 h( Y7 e0 v
Division rings$ D3 {$ k' \7 w- _ j+ L F* ^
Double Stone algebras
j- E8 j9 Z( T7 Q' i2 tDunn monoids
% ?6 H1 E" C7 [4 R0 T( Y, pDynamic algebras
: A/ R3 u9 f( \5 ^Entropic groupoids) W! v% h; s7 ^
Equivalence algebras
( F' [( z+ I- \' SEquivalence relations
+ _/ S" Z- [3 v b7 O4 Q' _Euclidean domains
- K2 S2 ]6 s$ G7 j1 F+ ~8 ff-rings
5 {: S( P2 c: T3 g$ R2 z" {Fields0 i( g1 [2 I+ N% z
FL-algebras
; P" `; X: ^* _0 f% U2 WFLc-algebras+ T7 @$ R; x# |$ C$ [3 H" l* n, r8 z
FLe-algebras
* X; X5 K7 [5 _$ BFLew-algebras
% K3 A, V0 D# D6 ~4 h# g+ g# PFLw-algebras
3 w; v) ]4 Z& o3 KFrames! q3 |! H1 d: m8 c/ \9 w
Function rings
$ L) \. m, g+ D @* p' iG-sets
* S: Y! Q5 |. }$ \0 `7 FGeneralized BL-algebras9 p+ e; w/ M: I3 a! x" I
Generalized Boolean algebras
7 |0 C0 B. t! e+ A% h& Z4 {/ T% Y3 [Generalized MV-algebras5 [ W+ P S6 @
Goedel algebras
- M V- f6 K( V. T8 i' IGraphs
# t6 r* o$ x9 @/ W2 uGroupoids
% n" B1 |8 _& f' c' U" \* R# ?Groups
1 ~/ h7 `- o. R$ Y6 IHausdorff spaces- @; ~7 F/ N2 U' W2 \' a+ o
Heyting algebras& h$ Y1 G9 m5 W
Hilbert algebras
7 N$ t$ u }& ZHilbert spaces
4 Z6 H6 ~- ]! b& m& c9 v/ E& XHoops
6 ?5 V% U1 O! R7 XIdempotent semirings
5 L& u) q1 y" D& zIdempotent semirings with identity
- [8 y0 M; M4 w# d( Y6 T @Idempotent semirings with identity and zero
/ o- X( o- ~5 k# AIdempotent semirings with zero
{6 i( ~7 [( \# B, dImplication algebras) h! L$ O) ?/ x0 o( ?/ [
Implicative lattices0 r% a& h) z" k
Integral domains' p0 g. g$ M' T( q
Integral ordered monoids, finite integral ordered monoids6 }; [# o5 Z4 f
Integral relation algebras
& t* J4 W9 {: F+ Z5 O) zIntegral residuated lattices
# }, ~% v) M. d# A7 l- H8 ZIntuitionistic linear logic algebras
0 W D/ e( e& _6 @Inverse semigroups, a/ E9 o9 p2 L" z. j& {
Involutive lattices
6 p0 ?% D8 Z+ k3 z( A) I f& uInvolutive residuated lattices
1 p4 \! }) }' g& `6 h! mJoin-semidistributive lattices; F8 @9 H9 p& ^) F. U/ m
Join-semilattices) R6 ~, D, ^& W# S! Q0 q3 I& G
Jordan algebras( D; x/ A" o8 E+ f9 c
Kleene algebras
5 V) z9 Y$ m" Y* s% ^* IKleene lattices
, G, p' c: y4 R0 uLambek algebras
& E6 r# k+ C& w% @( fLattice-ordered groups% z6 G; t0 l% b1 @- C4 L
Lattice-ordered monoids
! z/ b3 T; T$ H/ ^% ~; ALattice-ordered rings$ p% z4 L @2 u' E5 G) o
Lattice-ordered semigroups
4 t0 Z2 i& k( L0 r2 i* Q! ELattices
3 ~ ]0 G% m7 G" o& i; R `Left cancellative semigroups
6 D2 N4 A% q% D1 a6 R6 y8 JLie algebras' J! [2 k( Z3 G
Linear Heyting algebras
/ \0 c* ~- \- X8 PLinear logic algebras8 f( ]' K, z/ Z
Linear orders; r5 l6 A: p" S, b3 ?3 M3 [
Locales
. J$ Y3 x6 V* @. N! \; DLocally compact topological spaces9 y% q0 J' w1 X' |- F/ U
Loops
7 K' V- N8 e9 nLukasiewicz algebras of order n
; m. ]- a* y4 m) _# d' PM-sets) r8 w* r1 h; U/ [) Y3 ~7 K; z
Medial groupoids4 ]5 t+ N9 l6 ^
Medial quasigroups r6 d; x, m( W& Z% p2 e$ N
Meet-semidistributive lattices
: H' M% k: b0 L; SMeet-semilattices1 Q) l6 q7 ]: N1 o ?8 j. |! z
Metric spaces" s. [2 G! @( K$ ^8 x
Modal algebras
" _0 M# x" O: b. ?# d4 cModular lattices# h1 U; R N+ f+ E
Modular ortholattices$ x$ i5 t) _( v! V8 a$ v
Modules over a ring
6 h5 T' Z1 V* ^3 P1 W/ ^- ^: q$ {/ _Monadic algebras
* ?/ b# R0 G1 F% V8 M, d) j: |Monoidal t-norm logic algebras- l1 ~- f8 ~* r. W+ P4 Q
Monoids, Finite monoids, with zero% W( @3 s6 w3 U0 X" `. D
Moufang loops; B, o; M7 o$ G- X
Moufang quasigroups
1 F* e8 l! [/ iMultiplicative additive linear logic algebras! i, z5 F( r: v. }
Multiplicative lattices
( ]& M' D& h0 I; P! P3 r2 C, FMultiplicative semilattices
) f3 @/ e; {# N8 T n7 m9 f; PMultisets
: {: v+ X V. d. R$ B/ [MV-algebras* q2 }5 a! c: q6 ~" ~ L* Y
Neardistributive lattices
1 m+ [) \& J& x' m% A& yNear-rings
1 ~4 `! j7 W1 S9 p: ANear-rings with identity
+ Z5 p) Y1 I4 c% |9 p, t/ tNear-fields( T+ ^- [- r5 ]# Z' ]
Nilpotent groups& {2 G: i3 p0 r( j9 t/ J# Z
Nonassociative relation algebras) _7 J) X" k( D4 p/ s& x7 f# I! n
Nonassociative algebras
: A% |8 z& {" H3 C' A: I RNormal bands
$ ]. n7 o' G& k& ], SNormal valued lattice-ordered groups( G# `5 B3 P8 ]6 X! I" g
Normed vector spaces
+ N6 b* _% }9 m2 r; N, f0 pOckham algebras, d7 H, b( a) ^3 _
Order algebras
) g- `0 r. e) {2 S7 LOrdered abelian groups
+ K& L! @: N' [) r8 M0 r, rOrdered fields
1 I/ j1 b$ W3 Q% G& n& _Ordered groups
) Q* I0 V4 [ GOrdered monoids
/ Z2 P% b4 ?1 jOrdered monoids with zero$ r9 s, j) b6 ^& ~2 c/ n1 _
Ordered rings% n& X4 M. G. \( S/ V
Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero% |8 b) Z& U! V
Ordered semilattices, Finite ordered semilattices% D0 r& O9 }6 n: t
Ordered sets
% K$ S% i" v) P R( Z: aOre domains& f* H) j8 a. N* y3 F5 Q* h0 ~. p
Ortholattices
8 l' u4 X. u3 o$ T' a6 KOrthomodular lattices3 R' G- q& `! @0 h5 r; r
p-groups
! k9 V0 @! F" H2 J4 l- ?Partial groupoids
0 Q7 L! r( Z$ d0 e$ m7 W. K; BPartial semigroups
- \7 k4 E3 C6 o0 r2 ~4 `( aPartially ordered groups+ I- I9 {, u9 E: v* I
Partially ordered monoids f& ^* g) Q; Q- v+ D% U
Partially ordered semigroups' j% m8 R8 J7 N0 L6 X \; `* F
Partially ordered sets
' ~4 \/ P% s! l5 Q1 OPeirce algebras
" i) C m; k! @, V- c: e$ _Pocrims
, H+ E5 k4 M" A$ ?/ C1 @- p1 OPointed residuated lattices/ l& L5 a6 t* Y7 Z# f; K
Polrims
9 A+ h, {) ^% I9 DPolyadic algebras
9 ^5 p, \2 x Y& F" N6 vPosets
8 v" k% q. N/ BPost algebras
- U6 x7 y( t+ @1 x- xPreordered sets2 P* w; ^; w' H6 h
Priestley spaces
/ o, F l/ ?( w$ D# d$ \. T) \Principal Ideal Domains
& G; L5 M& ]3 U# C/ r! [* WProcess algebras
' v8 k2 B& N EPseudo basic logic algebras# R0 R G# b9 Y4 Z \
Pseudo MTL-algebras* ~6 r K o' b
Pseudo MV-algebras
, B$ w2 I' k) k8 cPseudocomplemented distributive lattices( o+ ~$ [5 K( L( Q; u+ @
Pure discriminator algebras
* n2 V) Q8 v9 B' @0 oQuantales
& g0 s( k, T* s2 u% q0 ~! nQuasigroups; d( p* ^* d2 @/ G6 u( x0 F2 o8 x
Quasi-implication algebras
3 W2 q0 C5 e* E9 [) |+ @* IQuasi-MV-algebra
" y, L/ B8 C% k7 YQuasi-ordered sets
# Q4 @% b( I0 cQuasitrivial groupoids# B: g. G1 C6 b7 t6 G, m
Rectangular bands
: d' n. |' l$ s t% O8 G0 bReflexive relations. x0 p2 H$ z2 c- Q0 L
Regular rings
/ Y5 `/ Y% ]5 ]9 `. u" `( eRegular semigroups# Y0 E# f& M( C4 O! l/ i* W$ w
Relation algebras
U- S5 {, n; q6 e1 s5 kRelative Stone algebras' X& Q `2 J6 d0 b
Relativized relation algebras
" n* {9 \9 B/ p' M8 r; Q, A0 _+ m. XRepresentable cylindric algebras# `4 i8 h$ P3 m' I3 F
Representable lattice-ordered groups; o8 G" X8 @: }' }8 i
Representable relation algebras
* y- a3 w: A5 ]: RRepresentable residuated lattices5 D7 _0 h1 h5 c. j0 \
Residuated idempotent semirings
3 }: R: T$ G- \Residuated lattice-ordered semigroups
. P0 L2 K' m2 M) {Residuated lattices
" r; f: M( {0 T# qResiduated partially ordered monoids" R" r; v! C- |4 a0 u" W
Residuated partially ordered semigroups* z, h; E' x6 ?% ^" q
Rings
4 g# A5 x4 E/ A. R, @6 ERings with identity
4 ~, Z- @: l' ]! K+ wSchroeder categories
9 m& j0 h0 ?' b( ~Semiassociative relation algebras! u4 J6 T# D! r0 q- C0 I( d
Semidistributive lattices4 b* Y: e% Q6 m4 r, U
Semigroups, Finite semigroups
+ W- g6 p; [* k e; P3 ~: f7 fSemigroups with identity
+ x; T, Z6 m4 A6 P: wSemigroups with zero, Finite semigroups with zero& N) s$ u0 i# o0 ?; r
Semilattices, Finite semilattices
9 v5 F0 R- k$ ]2 i5 }1 ISemilattices with identity, Finite semilattices with identity
, D$ I' V F. X/ [$ J _* j7 XSemilattices with zero( S/ L6 K0 \& ^) V4 R0 g( v- d* Y% ]
Semirings
* W3 W% v4 D' R5 e" | Z0 Y* HSemirings with identity
3 c- `+ l8 j! A$ g' y! U+ D8 SSemirings with identity and zero
0 B9 ~, k, O, t1 W/ _$ w. pSemirings with zero
& s, j! E( I6 y b L& `Sequential algebras
5 p* f$ K/ r' {9 i% g. s2 {) {3 |Sets
0 ~8 L: x+ z/ f9 s; c) x$ D# M5 DShells/ c$ G0 [6 L9 f# a! Z% @
Skew-fields' x9 o/ \# p A* {
Skew_lattices( q7 t. R9 L' n+ M1 [
Small categories
, q) e4 y$ P. R1 e8 gSober T0-spaces
, ~4 X4 q7 ~6 X2 q* @Solvable groups
: |1 E$ D- z F, Z/ B3 bSqrt-quasi-MV-algebras; b) N% ] K( ]" R, q1 o, a U
Stably compact spaces' o: `! h; o7 F
Steiner quasigroups5 K9 o! ~) q, {7 L3 X* V
Stone algebras
8 Z4 Y7 G. D9 A. a& k+ ESymmetric relations
2 I* Y1 P& e3 b% A8 TT0-spaces
2 w, C9 t2 V. \+ k& D7 R, ST1-spaces
; m9 _$ g8 k+ s& ]. X( ?& PT2-spaces
) @3 S' y4 p; \: NTarski algebras; Y3 x, x" O6 O% H: O# G
Tense algebras
" M+ b; t2 V4 \% F4 k8 F' _( ]Temporal algebras) C" a( y/ S8 e8 \
Topological groups+ s/ O# U" V1 _4 z
Topological spaces4 B4 ~/ P" c5 R
Topological vector spaces
) Y" y7 ]' d; _- rTorsion groups
* L4 Q2 C& D# j7 j/ W( tTotally ordered abelian groups. V* U( V0 {2 @+ S
Totally ordered groups) d' m2 b3 T& p5 c( u
Totally ordered monoids
$ H! j8 A2 i' \6 A2 @* d9 f+ QTransitive relations, S U8 E+ C. z/ `1 J
Trees
6 e1 C* D4 _# Z: p0 `4 @7 ^. ITournaments
0 _: A/ b2 G9 h4 ?+ y' V! R0 ZUnary algebras
! U* S/ o! L6 J/ I" [ u- Z5 j" `# wUnique factorization domains7 O- t( O. r" {5 j$ R/ y
Unital rings B4 @4 t" ~% y' p- w% _) t9 t5 w' j
Vector spaces4 i9 V5 {: x( {! \1 \: a1 Q- R
Wajsberg algebras
4 z# N# B* g) xWajsberg hoops
& F6 d1 b6 a# m) d; |Weakly associative lattices
+ M F6 o/ x" [) ]4 H+ YWeakly associative relation algebras
+ O) c& ?, l! M' X) {. D* a# dWeakly representable relation algebras
! ]3 G, w7 }5 s5 n# M! v |
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