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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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, l A8 {9 W/ U+ n1 S: a& R4 w
6 E$ ?( g1 E% D l8 [8 XAbelian groups Abelian group N7 [5 ] T5 v/ @
Abelian lattice-ordered groups
1 |2 q! h. [; E d/ \1 ?( [Abelian ordered groups
+ M0 s9 W; G& t) l+ YAbelian p-groups5 V$ r& f1 ~; `1 \; O8 x) w6 C, p! j7 p
Abelian partially ordered groups
, J8 c6 O7 t9 t$ BAction algebras Action algebra
) f3 B; H" a/ w6 YAction lattices
" J, e; n' ]0 X% ` S. J- iAlgebraic lattices
9 B1 Z. O- s) @5 ^8 P2 s: [" p* U3 jAlgebraic posets Algebraic poset# ]8 Z4 U; C7 r: s x
Algebraic semilattices
3 p8 x4 {8 ?& L) EAllegories Allegory (category theory)
/ y( H( N* S9 q- D4 k0 kAlmost distributive lattices7 l+ v6 K8 f3 I, K
Associative algebras Associative algebra
" p* m% m3 @5 Y; QBanach spaces Banach space! \% w8 F7 z4 |2 A7 j
Bands Band (mathematics), Finite bands' s* B4 l5 g1 M: w, ^1 C4 I" @
Basic logic algebras) v0 {8 `7 p8 \6 I. p/ y% }
BCI-algebras BCI algebra
& g; V) \2 i. s7 CBCK-algebras BCK algebra
* [' Y7 Q% I& [& ]8 WBCK-join-semilattices$ b" P2 I Z) u% R# F: {2 @
BCK-lattices9 b2 ?9 \" O+ E2 H6 g+ o
BCK-meet-semilattices
& l0 }3 R. B4 R2 o" k9 b qBilinear algebras4 e6 e0 |. S) g8 p; C
BL-algebras
+ m6 e( z' B4 z7 }* UBinars, Finite binars, with identity, with zero, with identity and zero, ' M6 a Y/ Z7 N7 e6 X d& W8 X. t
Boolean algebras Boolean algebra (structure)* t. ]9 S1 J( \+ u w( i
Boolean algebras with operators! T$ C0 _) j+ o/ o
Boolean groups& R- r( }0 l* T% U, y: N" k( @0 ^
Boolean lattices
. Z: D2 k3 Y3 T* ^Boolean modules over a relation algebra& v$ v" S2 ?9 v* V; ^1 x8 i1 r& ~
Boolean monoids& |$ P9 A$ @. i% f* E; F; z6 ^
Boolean rings
+ n/ O' X% h/ c! |: u5 W5 FBoolean semigroups" M0 D* t1 ?, [2 R
Boolean semilattices! K: [0 z" d! I4 G8 P
Boolean spaces
' t5 ?9 b" |* L: u6 X- cBounded distributive lattices
9 Y! |3 J' c: `! G% l$ L- yBounded lattices
' m5 [6 ~8 y1 yBounded residuated lattices
" L6 c7 M' y* n& {Brouwerian algebras4 _8 a; x6 r) g
Brouwerian semilattices
8 y5 b% h: v2 ~: z% sC*-algebras
- e1 H: E, y7 Q$ h# rCancellative commutative monoids0 {, A+ E8 k: \2 C( t8 J
Cancellative commutative semigroups% y( r# F- ], X% o/ t, Q
Cancellative monoids, b9 f( X! S: E3 @9 M' i4 a
Cancellative semigroups7 u3 H, A5 z/ e) J( \
Cancellative residuated lattices
) [0 \( G5 y. C3 dCategories
, w' k) E ]: o7 p2 @' \( D( uChains
+ V% j8 E% B4 `: [! E8 iClifford semigroups' I; j$ ?) n" V" R8 J1 l
Clifford algebras0 Q6 q) q3 W6 m2 Z6 g9 a
Closure algebras
( [- v' C9 V# _! w' D4 f4 V; [Commutative BCK-algebras
+ r0 X# f6 u* J4 C6 @2 dCommutative binars, Finite commutative binars, with identity, with zero, with identity and zero 7 ?. x& r; `. l! ]1 e% Q
commutative integral ordered monoids, finite commutative integral ordered monoids+ w% t. I1 o6 s3 J3 L! Z+ m# f. g: k
Commutative inverse semigroups
6 V4 d( E7 V- n) s4 _1 m/ _8 v8 tCommutative lattice-ordered monoids( r1 v, z$ A7 j* S! y# s; t" j7 o( V
Commutative lattice-ordered rings @4 b& |( s' p/ p2 `1 Z
Commutative lattice-ordered semigroups0 T; |) M- Q' P
Commutative monoids, Finite commutative monoids, Finite commutative monoids with zero) M3 w5 m2 ]$ Y2 O% i
Commutative ordered monoids- i! T# _4 i# R i( o- Y; N" ?
Commutative ordered rings
9 T# Y. p7 M" L$ oCommutative ordered semigroups, Finite commutative ordered semigroups
- v# B' K( y% @' Z% K; T0 U0 gCommutative partially ordered monoids
8 k5 `+ ?- t6 T% QCommutative partially ordered semigroups
. [& w! e% e3 F% w& TCommutative regular rings% i! q! S4 P4 v$ E6 M: e) I6 J- y
Commutative residuated lattice-ordered semigroups$ C% F- y1 j( b3 x5 `' N
Commutative residuated lattices
0 |+ M1 I& |, H9 y8 \ LCommutative residuated partially ordered monoids5 J% T$ C/ ^" l4 h
Commutative residuated partially ordered semigroups, O1 S9 L* x8 Q6 k
Commutative rings
$ \' L9 @0 s3 H" k9 t8 NCommutative rings with identity
, `! ?5 x: H+ u! K; d" G( yCommutative semigroups, Finite commutative semigroups, with zero
+ V, }1 F! T2 Q8 `# I. e5 G: uCompact topological spaces
/ C5 v4 L+ E# v0 h7 y# {5 V# UCompact zero-dimensional Hausdorff spaces
$ w5 x: O$ R, [, ~Complemented lattices
' M) x- A- ?% `9 }. I9 eComplemented distributive lattices
0 T4 e# n6 h+ x8 rComplemented modular lattices3 C9 v$ ^+ S7 H$ p! o9 W$ \ s
Complete distributive lattices2 a. ^4 n* b' ^5 [. \, b7 f* K/ l
Complete lattices
3 l4 {6 }' J& @3 aComplete semilattices D/ H3 \( q3 U5 S
Complete partial orders$ N/ H5 x2 x$ ~6 k+ K
Completely regular Hausdorff spaces# b! M5 k! }# P0 W) U
Completely regular semigroups
) Z; g/ z) d1 ~0 o! g. c1 S* bContinuous lattices% I& l# M$ l5 a2 K; ~
Continuous posets
8 b% z- J4 x) b6 i$ ^Cylindric algebras3 M2 @( A$ a A/ \0 A
De Morgan algebras
$ C s" W2 o2 I x& ^1 W+ ]' m7 FDe Morgan monoids
' y+ h: y9 e2 d4 K; F U; QDedekind categories: d/ B R# G) C7 S( o2 S$ b4 q8 [8 ]
Dedekind domains& {- K, u# X2 y) E1 l
Dense linear orders
# n( v+ m: D0 c$ W. aDigraph algebras4 n: [# H1 D6 P" X# U! ?: }
Directed complete partial orders5 x& q+ {/ U' G8 I+ i1 V
Directed partial orders* D& C2 W f4 J( ?* V6 x
Directed graphs3 k2 {6 W% f# W, `4 @
Directoids
7 j3 t' e- |- x* bDistributive allegories
$ ?+ i( V8 L' wDistributive double p-algebras
7 }9 M7 v/ L% E6 U' z* X. hDistributive dual p-algebras# f l4 F' R$ [9 R/ [( g
Distributive lattice expansions
6 p. y, h- ^* V6 c" A u d1 w$ BDistributive lattices
8 W. E8 W' e. C$ BDistributive lattices with operators
8 ~' n4 S0 d0 Q- P. HDistributive lattice ordered semigroups
+ n) ~% I' ^( E9 |# s b) @Distributive p-algebras
0 s8 b8 ~0 W7 h, K4 \2 l3 |6 f5 lDistributive residuated lattices
( ^% u5 x. \9 O9 d# G B) W `Division algebras4 N- h; g% c; i
Division rings1 v: ]4 ~: v+ u- ?6 c7 i
Double Stone algebras# t: t& A d9 Y
Dunn monoids& j, S1 J* r+ e: _
Dynamic algebras% N3 v- [! |/ R) e
Entropic groupoids9 I. Z0 T2 Z3 {7 f% K
Equivalence algebras/ `- e6 i2 L# H9 e, S
Equivalence relations
* H3 @0 _5 V4 l- AEuclidean domains0 S- |% g7 M; @% J
f-rings
6 u7 ~9 ~& q4 ~7 n9 IFields: t4 z1 A5 T$ @
FL-algebras7 I W& G- H3 @; ?
FLc-algebras
) |% r. {! Z8 ~7 i0 \7 oFLe-algebras6 j, E) }7 R* k+ E, Z f
FLew-algebras% R& T7 m4 D7 S$ ]. L
FLw-algebras
) N6 \# h& @, d# Y7 |/ h) g2 y8 B) uFrames
7 I+ |" i. Y, L, {+ ]% v* P. W. IFunction rings
% X1 `/ s, n" y7 D! O+ vG-sets$ L! o+ |, J' r
Generalized BL-algebras/ q: Z% _# K+ t; N4 B+ x7 |( h
Generalized Boolean algebras
0 G' O% I! i9 R uGeneralized MV-algebras0 v' ?, F7 W$ v% Y2 L* i
Goedel algebras5 X. S# A% ` j+ Y8 i* d- A4 F
Graphs
7 `/ D- q' G7 }+ j" P @" \Groupoids
i, p/ N+ S) `$ I- `' y( JGroups2 N7 s# x/ J# ?- D6 V
Hausdorff spaces, q/ e* P" n+ Y: j! w
Heyting algebras# T1 {$ I5 s6 `* ~5 t2 F
Hilbert algebras
$ K \$ E* j b9 ZHilbert spaces' A% k6 c4 R( U
Hoops7 p% @1 W: F! W. O
Idempotent semirings8 b! \! c: _; q$ j" [8 G3 N+ X
Idempotent semirings with identity3 |& o9 P$ G# ~* ]. w: C
Idempotent semirings with identity and zero
8 V0 i. A. H! q0 h3 D6 {/ PIdempotent semirings with zero! E4 Y, U3 b) M9 i" ^1 m" l
Implication algebras( T! h" ]& X, {2 P( v
Implicative lattices
7 G9 g w2 U; \' g, [3 ]Integral domains8 ]& |$ m: o& a7 c8 c
Integral ordered monoids, finite integral ordered monoids8 i1 z# U3 \9 @4 `4 ]
Integral relation algebras
% T' l( z/ F6 zIntegral residuated lattices7 p3 x0 n6 T7 [1 |. r$ k
Intuitionistic linear logic algebras
* a' t$ u/ o4 ^1 t8 @Inverse semigroups, p4 ]. v/ b, V" Y( V
Involutive lattices: W5 G8 {. |* x8 Y" f% K
Involutive residuated lattices
' K Q7 e# a. D' I3 UJoin-semidistributive lattices5 ~* K& M. {/ ^- W7 D1 g1 ]" }
Join-semilattices* z$ r. v% y* x2 D/ w- \
Jordan algebras0 w: t. W' E. j
Kleene algebras
9 t& H* {+ D9 J/ G9 tKleene lattices
$ u7 l2 y. v- pLambek algebras
2 j7 J( x7 \. m/ RLattice-ordered groups, u8 B0 ~# [# S5 H, e5 D( v0 G
Lattice-ordered monoids
& h( |3 ~% c& @6 F6 {Lattice-ordered rings
% b' ~- L6 T7 N* `4 g4 ZLattice-ordered semigroups, v% M1 K/ o! Y1 ~& ^
Lattices
" p8 L9 \) p: j% z/ ]Left cancellative semigroups
. B S7 E5 i+ p, \% Z% K* P6 R' g# ^Lie algebras) O9 w; l5 N3 N$ K
Linear Heyting algebras# w5 f F; A; H3 ~- j H
Linear logic algebras
& B3 N( \2 ]+ K' N( T" fLinear orders
7 Z8 B9 \* `* w0 tLocales) D, ^/ h7 O1 l% ]/ R
Locally compact topological spaces
* q# r! n/ Y x. q5 TLoops* ^4 _7 L2 ~; j; R o+ `* V/ C
Lukasiewicz algebras of order n+ A- u0 w; W, T3 U. ?1 a; I
M-sets
0 H8 r0 E1 t) v8 u) b, RMedial groupoids2 H1 p% I; c& ^3 z3 `) ~3 x7 V
Medial quasigroups" T$ n+ z. \; C
Meet-semidistributive lattices
" o4 i. g0 V' U8 f u% n0 F# \Meet-semilattices) g. k3 j3 ?+ S7 V1 e$ [2 |! ^
Metric spaces
- t7 l- S- A9 J& I( SModal algebras
/ ]" W) @/ y( J! G- z lModular lattices7 T, v- h% F. _7 K J
Modular ortholattices
( k1 b" ]! I( q0 W& `, t, U9 w8 ~Modules over a ring% S X5 B. V8 @+ d
Monadic algebras
. v ]" l5 h# l5 OMonoidal t-norm logic algebras& a* n* g; k% L& k: A5 s
Monoids, Finite monoids, with zero
8 W$ [8 Q- k. P( ?- vMoufang loops
+ d# q* ~" k6 l7 R8 ~Moufang quasigroups
' j& W ?& a5 YMultiplicative additive linear logic algebras
8 I7 Z. o" O& @2 H7 X/ d" @Multiplicative lattices) s% B/ h+ l- K: G
Multiplicative semilattices
7 l* m; r+ e4 s+ k/ L% ?+ QMultisets3 y! S' U* d) c. f! o
MV-algebras
7 H6 g. `9 d2 W' ` ^Neardistributive lattices+ N0 Y: d- O* _2 @5 D5 P! B# Z2 r$ n
Near-rings9 ~" }9 _6 T2 z# {/ L0 C5 H! [
Near-rings with identity
& C# Q8 f: p9 @* ZNear-fields
. K4 p, Y0 O, q; oNilpotent groups/ Y* y5 ]5 H. B
Nonassociative relation algebras
) n2 u3 h! c [& c7 _, bNonassociative algebras
# r& V1 k( v; w5 @5 LNormal bands# } t- V/ x% M/ t- b. I9 Q! K
Normal valued lattice-ordered groups5 X9 P$ U) a& ~" K% Y$ _
Normed vector spaces
0 W, T% E g e( ]$ [# _ TOckham algebras% t% r4 q! |% ?8 n# n9 J
Order algebras. a( [, X. s& i; F# s
Ordered abelian groups
, j! m x, [, f) l* \' }! ^7 SOrdered fields* ? F4 E W% l/ t3 T2 Q
Ordered groups( ]& g- K& } e
Ordered monoids/ V& o1 k0 m. @! X6 { u2 b
Ordered monoids with zero. D3 S% s, d: O" N5 _
Ordered rings" o- E+ ^7 D9 X+ B1 D
Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero
' `% k7 b( H+ U& y9 c1 M' q; T$ f9 YOrdered semilattices, Finite ordered semilattices1 E# Q" K3 V6 ~
Ordered sets
6 p" x' L8 K8 vOre domains
& q% |. f9 W/ R4 W2 g( X2 OOrtholattices6 h4 K D7 L6 C. V. A" J: B3 A
Orthomodular lattices
# z% f6 Q* [" H3 q3 i+ v0 ]3 ep-groups9 P( N: ?8 F J6 R7 s* T
Partial groupoids
- a/ S6 A0 z' }, E8 M9 JPartial semigroups$ c) H9 i N5 g7 ?* H
Partially ordered groups
2 P6 z6 _! I8 p- J' I* S5 ]* bPartially ordered monoids
- Z& O& x; L* m; Y0 X! O. pPartially ordered semigroups
* s: k! ^9 F# L+ o/ _Partially ordered sets
: U( W4 n% k7 p2 P# |0 J6 ZPeirce algebras
: e/ j1 d$ e6 ]% hPocrims
8 t) }( s) G" |5 l, J, B" [Pointed residuated lattices
' h4 L+ q* E8 } c. uPolrims
3 `! `8 h2 C4 J+ hPolyadic algebras6 B" [& B# W/ b
Posets
7 X' f j$ B. H! E: oPost algebras
% T; R$ g6 h6 xPreordered sets! t: `! }! n+ _
Priestley spaces+ S6 M6 T& S* t* T% I0 v# }
Principal Ideal Domains
+ @9 ^2 O0 l* R8 z2 k* I! xProcess algebras- P8 L. J* l6 L+ ~2 Z+ M
Pseudo basic logic algebras
) D) k: j. w6 n+ tPseudo MTL-algebras( B/ `% w' x8 Y. f. l; Y1 F
Pseudo MV-algebras N& @( i* A" G* x6 H1 U8 Y
Pseudocomplemented distributive lattices
6 O4 f' ] l- `9 c" Z$ bPure discriminator algebras
k* U& q3 M7 O, y" Y% N* S% | x# T# t5 rQuantales
% \& z7 G$ t/ r( `Quasigroups
; B2 e8 G2 |6 _7 b7 SQuasi-implication algebras1 c' z6 K# U) H
Quasi-MV-algebra
3 o- R9 r( Y0 Z! i$ W( g- RQuasi-ordered sets
6 z3 g3 w( a* K3 W( N3 JQuasitrivial groupoids
@0 }+ v5 Y% L4 H+ W; y3 sRectangular bands1 p3 T" K' E M2 O) A5 A' m
Reflexive relations
4 K7 E. C {. l- ]# h# L4 P7 h9 sRegular rings4 i" I' p9 D7 q2 d, c) j9 [
Regular semigroups- `- _+ q* F) T% b
Relation algebras6 t3 n1 z; o2 j+ X7 ]1 q: m
Relative Stone algebras! _' Z- A+ S( A# P7 G
Relativized relation algebras
: l- ?/ _4 D. Q4 S& }6 V# I1 rRepresentable cylindric algebras
8 \! U/ X4 R, YRepresentable lattice-ordered groups5 V4 S4 c4 S6 @4 D
Representable relation algebras; b) W) S- b1 g: v' e
Representable residuated lattices
: R* V4 q9 q7 k8 |2 PResiduated idempotent semirings
) G' Z9 H. X+ }, l! Q( WResiduated lattice-ordered semigroups6 ]( {+ @. J3 Y: G) m" M4 J
Residuated lattices* ^ E# _" }& j
Residuated partially ordered monoids
+ p+ _9 Q1 D$ }$ p: F* iResiduated partially ordered semigroups1 `6 B. a5 m' {$ }0 H0 @
Rings
9 C+ y: G$ T7 J. x/ ^8 J7 GRings with identity5 T% P3 w# n5 ?2 X7 o9 `
Schroeder categories# `2 V5 X, q2 F3 e9 s% ?
Semiassociative relation algebras+ [9 K) }7 T! L
Semidistributive lattices- a) s( K# ?! h9 ~- h/ g& z
Semigroups, Finite semigroups* ^! J$ x/ X x4 z: G( O; b
Semigroups with identity
! [; C4 J! ?1 P9 t; d8 m* xSemigroups with zero, Finite semigroups with zero
O1 B" f; s# Q6 n9 hSemilattices, Finite semilattices9 F' t g( o' P% P' ~
Semilattices with identity, Finite semilattices with identity
8 G# n8 z4 P! d) b" \& X# u( H# z, x( {Semilattices with zero4 U* g9 k( u- w
Semirings' D; J2 P. y4 d4 D# C0 q
Semirings with identity
$ _5 n1 ^* e2 \( R/ r( xSemirings with identity and zero
2 A. q: o8 ] cSemirings with zero
% w. e' q3 U0 `7 }9 p- kSequential algebras2 J( ]0 R# j# O* e- O) `. w6 S
Sets
" r" [# U8 Q: ~ i& aShells
3 H. {9 G M9 g3 aSkew-fields9 O5 N. ~( f- S3 {; `' }1 P
Skew_lattices2 x0 ?- I& b' y) N
Small categories
9 L0 r7 R8 m5 t$ u3 b& L$ DSober T0-spaces. y4 |3 }* o( ]. s) }4 _$ u6 |) S1 ?
Solvable groups2 ^: w9 M8 Q9 n9 C' I2 A( Y% e
Sqrt-quasi-MV-algebras
# O3 e! R' ~2 ?" ?! LStably compact spaces; b; l3 \% f- f V$ s* q, P
Steiner quasigroups
, u6 t. \6 F6 W3 ]3 CStone algebras
6 r$ L Y( F; ]$ kSymmetric relations: U' R* k# ^$ S6 J
T0-spaces1 ]$ Y; m& d: ~( C+ s
T1-spaces+ k% ~7 y" M8 Y( e2 l- w
T2-spaces
$ A3 X, P8 z3 f; u3 G9 r+ oTarski algebras
4 v5 J1 Z7 ^& Y" D- L, \ j/ m" rTense algebras
: s. E0 f: P6 XTemporal algebras, y/ w' w5 k' ^( x! r/ N
Topological groups
$ E; I8 l1 x) @. i. P# W( dTopological spaces
/ |. d* J+ o( p4 ?Topological vector spaces. F2 v1 m( \! u7 x1 P
Torsion groups$ F, p2 G; J0 g' L" V
Totally ordered abelian groups
8 y) A5 U" X# i& ?! HTotally ordered groups3 S& T' y* v9 ]" [& `
Totally ordered monoids
% J) b M6 _9 @' `1 H) \Transitive relations; {$ h1 |, ~$ N( Y
Trees
+ V6 I5 W8 _7 CTournaments
8 S* e8 o4 _+ W0 sUnary algebras
V+ x' x# Y% a* [0 uUnique factorization domains
3 @5 ]& Z( o7 B: h! m" s) kUnital rings
# Z2 ?: Z$ m( A& _6 PVector spaces
) `8 Z, @, [( A/ GWajsberg algebras* o% Y" }0 }/ I! u- w9 }
Wajsberg hoops3 ~; h* _6 ], }3 K, e
Weakly associative lattices
1 _; K' Y, T( |- v) d# S7 D: JWeakly associative relation algebras
7 @- a7 _# v' l2 }1 L OWeakly representable relation algebras% I) A: C3 b4 S/ n$ Z6 X
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