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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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$ C2 i% F+ z7 b6 o! `0 Z
# ~, }' x/ a2 H @3 b
Abelian groups Abelian group
. q6 e0 k$ e i" t6 M5 |Abelian lattice-ordered groups
$ ]# }" x3 B& p/ RAbelian ordered groups8 }! D; ^: t/ k0 I i( y
Abelian p-groups/ {" A2 g7 ~2 J0 S7 O* _: `
Abelian partially ordered groups! u( n! r4 G. M- z
Action algebras Action algebra/ _* M+ G0 ?; d; O# Q
Action lattices' l1 S2 W/ }, z9 \ h, H, p! o
Algebraic lattices
" o# M) y3 V9 }; GAlgebraic posets Algebraic poset$ z8 l! L; O; O" S8 E
Algebraic semilattices
* U: M7 P8 }$ O* fAllegories Allegory (category theory)2 `2 B6 q, F; t& S0 c0 B
Almost distributive lattices5 i* J, E L& ]+ J N% q" O
Associative algebras Associative algebra
$ Z& l6 t+ i5 N3 P/ A) SBanach spaces Banach space
v. x! r+ P. SBands Band (mathematics), Finite bands
8 l- m- _2 ~8 H" X+ zBasic logic algebras
2 T( y2 m( [3 w1 }BCI-algebras BCI algebra8 L a3 u: W* t5 T* w3 V% \
BCK-algebras BCK algebra
3 |- a" T- R0 z' r3 NBCK-join-semilattices
8 c( o- P0 C2 l# s) w/ T HBCK-lattices
* ^1 x! l/ S7 g% s; TBCK-meet-semilattices$ v0 u1 s7 `+ _
Bilinear algebras" B: M, z/ T8 d" M" O. d
BL-algebras
& ~$ j4 P7 _' Z, |# V! CBinars, Finite binars, with identity, with zero, with identity and zero,
0 g: y. Q7 [! D- X+ W8 [% ?6 L; |Boolean algebras Boolean algebra (structure)
% Z$ d" R& P6 g- P9 X& g* ^Boolean algebras with operators
9 A7 r( o& Z8 w1 ~. [4 yBoolean groups+ A. a8 O0 ]6 A% @9 v
Boolean lattices( e/ @- P1 {! h8 p* L% Z" T
Boolean modules over a relation algebra! D$ A4 K: i j, z1 @/ L
Boolean monoids" j) x8 x* j0 g3 D2 ^) v
Boolean rings0 j1 Z4 U0 ]7 V5 B8 ^; ]5 y A" R$ w
Boolean semigroups
! [* g2 I" c9 xBoolean semilattices# {+ p* G) y; Q y
Boolean spaces
; Q' S8 |7 m0 MBounded distributive lattices3 y( v% R, l9 x) L5 `* m4 c1 f- N
Bounded lattices
- f3 B. x* Y; R* s. h1 lBounded residuated lattices8 e( U2 {$ p* }- k& _& X- J c
Brouwerian algebras
9 z( s( ? `- F1 L) |! GBrouwerian semilattices
% }. `2 F7 x3 a. M: w' oC*-algebras
! Y* I6 ^1 k. ~4 LCancellative commutative monoids2 _# ]5 H4 T/ l2 Z0 x$ f* B
Cancellative commutative semigroups( z+ n+ |# a9 f, W, r2 Q. _" q
Cancellative monoids5 N* {) g. `% J
Cancellative semigroups5 K0 J( W* o4 a7 u% f1 l
Cancellative residuated lattices# l$ @, e$ o* W+ @ R0 B2 P
Categories3 z |% }% d- j3 j# L
Chains
5 K+ D: @0 b) X4 q! z: [; T- pClifford semigroups. W! h5 p% m2 j9 J8 m8 f3 ^! {
Clifford algebras
* H8 u. |/ A; K$ c, iClosure algebras$ R) C' c; h2 Q
Commutative BCK-algebras; e% w5 c+ L. j$ R# s$ \
Commutative binars, Finite commutative binars, with identity, with zero, with identity and zero 3 ], F: @$ D3 ^
commutative integral ordered monoids, finite commutative integral ordered monoids/ q2 {/ h( V0 A: U
Commutative inverse semigroups
0 @5 T/ `% _0 B0 V+ mCommutative lattice-ordered monoids
3 D( r2 q1 Z0 Y- |Commutative lattice-ordered rings
6 M1 @4 Z" _$ gCommutative lattice-ordered semigroups& q& S5 ?- m2 S# d& @; @
Commutative monoids, Finite commutative monoids, Finite commutative monoids with zero
; b' }7 g* j, Q" l9 o: i/ @Commutative ordered monoids+ ^" F) j! i- g z- S) `7 G: }
Commutative ordered rings
1 {: b5 p& v9 Z1 a- s1 OCommutative ordered semigroups, Finite commutative ordered semigroups, v; Z5 h6 D5 [# u
Commutative partially ordered monoids
d$ Q- C/ Y5 N& ]Commutative partially ordered semigroups
+ p# _/ f$ \+ TCommutative regular rings
7 l! N: a, s, q0 k9 I. X f& R4 Z1 LCommutative residuated lattice-ordered semigroups
7 \' ^ U; Z( u0 N- oCommutative residuated lattices
! q6 J+ E4 v# m* @8 I2 h/ WCommutative residuated partially ordered monoids$ P! B( g$ C0 i. ~" ]. n9 x
Commutative residuated partially ordered semigroups( ]6 ^, G" D2 A! T% o) b
Commutative rings2 B# F* |3 q: S, r9 @1 y3 E: z# Q5 L0 }
Commutative rings with identity! Q0 a& }+ X" Z8 @3 t, L
Commutative semigroups, Finite commutative semigroups, with zero
7 T7 K0 j' E, y2 W; SCompact topological spaces
5 _ H2 M6 _9 J. U! Z; e9 VCompact zero-dimensional Hausdorff spaces
2 v: j! P: _$ l+ a0 b5 L# w0 tComplemented lattices
! V+ A1 ^: k6 `0 PComplemented distributive lattices
* C9 S8 B$ s- P! Z: n( H# JComplemented modular lattices
. ~/ R' S6 @9 K$ hComplete distributive lattices
4 y9 L0 c4 B' k% n# \' c- T3 lComplete lattices# _/ z O9 m A2 F9 d+ v" Q) m
Complete semilattices4 S4 `4 {# e$ O( Z+ v g) _
Complete partial orders
3 r& O5 ]+ v8 r0 w& QCompletely regular Hausdorff spaces
$ W, o$ o5 F/ C9 Y e4 T: @Completely regular semigroups" Q" ^ c1 }* j3 h X7 W$ p
Continuous lattices- k- z# L* ?. X1 P% B f" M
Continuous posets
- q' m e) _/ R* A# N' JCylindric algebras
( h! t' X! J) a9 i/ T' rDe Morgan algebras
. h8 l' s3 V0 `6 ^! z' P, S' R, WDe Morgan monoids) v* H. G. Y/ C- |; O
Dedekind categories! w; k( t; C* w S4 k2 o$ c9 D
Dedekind domains2 z3 G; S1 h. F* `! t
Dense linear orders( X' x% x+ ^5 c; M) s2 k
Digraph algebras
- j4 l2 ~7 h1 A( yDirected complete partial orders+ O) P5 B6 K: w- e6 x5 p/ m
Directed partial orders
. ?& I' S/ \$ E& U& ^Directed graphs
^7 ~ ]" g$ p! K3 MDirectoids1 z( L/ B4 j2 U6 p; X. }0 V. T- j
Distributive allegories& Q2 u9 L. y9 l
Distributive double p-algebras$ m. o+ s% `: S6 o
Distributive dual p-algebras
" N7 s2 q% o" P7 f) S( U. X4 QDistributive lattice expansions
( _( O z1 |* [( B& lDistributive lattices0 L& ^8 T! O- X, R. j
Distributive lattices with operators1 c6 C. D4 t) C
Distributive lattice ordered semigroups. k. @5 r$ F [0 Z, n4 G
Distributive p-algebras
0 p5 `2 Z4 n' Q4 aDistributive residuated lattices
' Z6 w4 I; `3 X- n4 r$ j; F) ]Division algebras: x5 s0 X7 s7 {! u$ c' h
Division rings1 k7 w2 m+ P0 T; k1 y5 l
Double Stone algebras: I6 ^/ D6 o9 L" E
Dunn monoids) w& }* C$ P* G( R3 G; J9 d* r! i
Dynamic algebras# J9 w: [- Z p2 ?
Entropic groupoids
E5 J2 h% s; [, sEquivalence algebras. P, q8 @! R" }$ R7 @7 z7 [
Equivalence relations
5 G2 A1 O0 H9 R5 d7 m/ KEuclidean domains
/ L( Z# F! k- Q- H% D: p7 |% Of-rings2 N, u% t4 ]4 a- ^' l2 K
Fields1 O( S1 t7 ~- S( ]/ {- z
FL-algebras3 ? p! `6 Z' V) e( C
FLc-algebras
1 j5 R% V i" ?+ i6 \# |FLe-algebras
: P% X7 y! f# e7 Y4 B$ MFLew-algebras: r+ }& a4 e! l# D+ T- V B
FLw-algebras
* v, h. O. f. IFrames
`- V4 |, ^- [Function rings
4 m( n7 p! G. J5 ~, XG-sets0 I' V3 u! M b `# r( _0 t
Generalized BL-algebras6 B# }: m) d, ~' H' `
Generalized Boolean algebras! n1 V5 V# m6 n4 `! V+ d1 X4 N
Generalized MV-algebras& Q E" _, \7 A6 X1 g! L
Goedel algebras
3 B7 m4 |5 Z3 r" P; a5 d+ B$ JGraphs
4 m3 A$ s# G! y, Z: D9 d# lGroupoids* _: [: _9 U# O$ o
Groups
2 Z- W% f3 W+ O& R' zHausdorff spaces
0 m, W$ p/ p0 eHeyting algebras
. C- r2 B# ~( @5 d1 \9 V6 A+ v QHilbert algebras
* U0 I \0 |: jHilbert spaces. S) q6 ?9 t0 Y! U) P! c
Hoops
1 p+ Z, q4 @( ~, w, w" b# [4 u* Z+ DIdempotent semirings Y. I. \8 b8 o- ~% Q) q
Idempotent semirings with identity8 Z8 b; h: J# I% `( G' n
Idempotent semirings with identity and zero
$ F/ L) o- j, `7 L* {Idempotent semirings with zero( X, | P P* d4 x5 Z% ]
Implication algebras
7 }, ?5 i$ T3 xImplicative lattices
% @; H* d1 Z! ^5 jIntegral domains
* C( }2 Z/ v3 O7 Z8 \& ?Integral ordered monoids, finite integral ordered monoids
) ^* E6 r G( F. I c# jIntegral relation algebras5 d+ `$ ~# a6 P* g/ l F
Integral residuated lattices4 T4 Q2 O) C; b8 W! I" m9 K9 f
Intuitionistic linear logic algebras+ D( d, R9 @- Z+ `
Inverse semigroups2 D1 A x4 U- S& Z4 ^! T8 O
Involutive lattices
% S2 m% _ r2 AInvolutive residuated lattices8 E- @5 I# T; I
Join-semidistributive lattices- K' z% ]) M5 ? L4 l5 [/ [
Join-semilattices
2 e4 A( _. E) L9 }, kJordan algebras& ^, T0 |+ l4 @
Kleene algebras6 u: G" e0 d7 \' D; N
Kleene lattices
) N- ]2 c* y- u5 }3 A8 }5 C6 jLambek algebras1 W- k' r# n# b# k' o
Lattice-ordered groups7 q# r) G0 T- a
Lattice-ordered monoids
8 i0 D( B1 k, i! O0 ~Lattice-ordered rings i: d0 {8 t! B$ k$ T
Lattice-ordered semigroups
* y9 {) l; P# I' X/ r! \Lattices
7 v! q/ H3 U% R' O4 ]Left cancellative semigroups; i0 Z3 ?6 m# @; M& Y9 g
Lie algebras
: x v h* L" v0 e7 R2 |3 {Linear Heyting algebras
& `% l3 _$ c( l! \! l* kLinear logic algebras" G+ Z4 s# J! B9 V
Linear orders# w& e) ~5 Q+ k' m
Locales' S' I* F; C6 W4 O
Locally compact topological spaces: Z X+ P5 j! n
Loops
1 S# j7 A4 X [Lukasiewicz algebras of order n" x9 _/ V! w1 m; [$ t
M-sets. a$ {: e( r- ^
Medial groupoids
0 h) g; u$ z# P/ d! i: b, ]Medial quasigroups
' I M8 v' q& t3 XMeet-semidistributive lattices9 R2 J! c' m$ ~" E: s7 D4 @
Meet-semilattices9 s2 ^ T4 `5 `
Metric spaces! f$ {# K, b% z: w
Modal algebras) z( i# }1 t( s) _
Modular lattices
' N6 F; V8 d* x* I' Y' o/ e4 SModular ortholattices
& }% z: `0 z" P# ]/ y X9 |Modules over a ring
( E9 N* |! O% MMonadic algebras
$ a7 p5 x& d" EMonoidal t-norm logic algebras, D8 T3 V' |! H
Monoids, Finite monoids, with zero5 s( e0 {; J9 |2 D
Moufang loops9 e0 \9 U/ R. }: `7 M6 w7 G
Moufang quasigroups a) {# H" Y' Y# i+ s3 e
Multiplicative additive linear logic algebras$ \) d; W! A6 i
Multiplicative lattices
6 t) g: S" ]; K0 e5 n9 W9 h- G1 LMultiplicative semilattices8 X" p) i& y% H
Multisets) F" p7 `9 g& X8 ?0 b3 e
MV-algebras/ b' E/ C* X0 b; z4 `
Neardistributive lattices' K/ I- O1 v6 m" L [. l
Near-rings
! F& q( L$ r1 w- jNear-rings with identity- d1 w1 I+ _7 W2 t1 @2 w
Near-fields$ I- T# R! J& q7 t( h
Nilpotent groups
( i: p4 f. B/ H; @6 b, ~Nonassociative relation algebras
) d" k" T$ G4 i" bNonassociative algebras
$ h) {% F, [; F4 Q6 `5 H x& gNormal bands
. L. Z" V. k$ {6 {; X- C+ V# rNormal valued lattice-ordered groups6 m+ z6 p: _ h8 z% Q7 Y* y$ h
Normed vector spaces7 \: g( t! H* A9 i2 x3 L8 r# b
Ockham algebras+ C7 L3 V' x2 I- b9 X
Order algebras, V# o" r6 o. s% D: v8 S, Z5 \( }
Ordered abelian groups
; X/ S o4 F/ O2 AOrdered fields) `) _7 L5 J) m1 _# @& h6 j
Ordered groups
$ o, r- |4 c) k" E* b( lOrdered monoids
8 A9 e7 m& \4 T) h2 [& ?1 qOrdered monoids with zero
3 U* G1 `2 m' _( l# MOrdered rings# G. o; ?/ W5 Z/ ^: W& E
Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero
& |/ ^3 e7 `% A/ KOrdered semilattices, Finite ordered semilattices( F( }7 ]$ I! K9 l& T# |
Ordered sets: l# M0 F! Q# P! {
Ore domains
$ Q2 d3 Q* a IOrtholattices
. X7 L) n9 r9 ]* W mOrthomodular lattices: ^' ]$ E0 u8 x7 H. P
p-groups
) @1 ]% H6 ?1 c4 [Partial groupoids
) |3 A4 ?1 I* L. Z6 gPartial semigroups
5 T: g- y u8 QPartially ordered groups
: M" Y3 f/ s) j. F% BPartially ordered monoids7 P! k2 p% A0 F" Q
Partially ordered semigroups
7 b) g' K5 l E: m: q4 rPartially ordered sets
9 }4 v6 _2 H3 TPeirce algebras6 _- p- c6 [9 j$ v4 [4 f
Pocrims% K) S9 N- f+ `
Pointed residuated lattices
( A& V' D* r1 ]* G, T4 [& B8 WPolrims
+ K; m3 m+ H5 X5 Y9 K' ZPolyadic algebras
( F0 f4 L9 `- m4 }Posets' B5 ?) f; b9 N+ N
Post algebras$ U* E$ M! ?- @4 P7 C
Preordered sets& L3 K v# e4 M9 k- T2 r7 n
Priestley spaces$ m3 }& S* l- c' ]4 T8 j
Principal Ideal Domains7 v' ~) s, Z* o( L( w) {- O+ E% R4 k
Process algebras
* h, Y5 |2 _0 ?$ Y: v2 |% lPseudo basic logic algebras
# ]& P# @0 `3 z d* T0 S" L; EPseudo MTL-algebras
. d( D& V- z. a, L/ u L3 a5 q3 n5 ZPseudo MV-algebras
! o$ u" H2 b# ePseudocomplemented distributive lattices* a& e% |6 I/ b) @
Pure discriminator algebras
/ G( u/ z0 c% y* Q7 ~! RQuantales) V# Z% o, }$ `
Quasigroups* j! D# O) M8 P% Y7 k
Quasi-implication algebras
- F% b( d5 B/ a6 ]6 F9 s: o y; R0 WQuasi-MV-algebra
+ C: ?$ {- z$ f5 V# A0 F; D. ^Quasi-ordered sets
$ T5 h* A e2 j; x# A* Y7 FQuasitrivial groupoids
3 h1 G* a* Q3 _% c! f9 ERectangular bands3 D. ^: n+ c, H. \$ ~
Reflexive relations
' f( Z8 r- \, w* d. DRegular rings2 y: S5 k* j# L/ T
Regular semigroups
$ s; M& Q& ]0 ]5 p8 aRelation algebras E/ A4 v8 D5 I* [3 x, \0 b
Relative Stone algebras3 |1 H% p$ k n5 X$ V$ @( y
Relativized relation algebras
7 v( c8 }7 P. t7 CRepresentable cylindric algebras8 p1 J; M* T6 X+ x
Representable lattice-ordered groups% C% H" a3 b% y# y. X; G3 R! W5 Z. k
Representable relation algebras
4 U" L' N2 S% I+ m+ E/ j! BRepresentable residuated lattices
- `, W- n, c6 }; @ Q2 v* iResiduated idempotent semirings3 q7 p2 W! U$ U) g6 X
Residuated lattice-ordered semigroups A% m4 [! L5 y. _" R( ]+ K
Residuated lattices# b# q8 w4 x2 ]0 J
Residuated partially ordered monoids
; u. c; s# i$ `1 MResiduated partially ordered semigroups4 ~5 H/ h/ u% P, w0 j( [
Rings
: ~4 W1 ^! h! P2 z5 u: t! T, BRings with identity/ h5 P+ R0 @0 L/ {: l+ h
Schroeder categories+ X8 {7 H& S3 v
Semiassociative relation algebras# @5 x1 z A$ {, \+ G
Semidistributive lattices }' z. K) L3 j, D
Semigroups, Finite semigroups- d& l4 o( {2 w% a0 j- q9 ^
Semigroups with identity
+ t' h" w O- W7 P- k+ bSemigroups with zero, Finite semigroups with zero: p8 i; G5 F) a1 b- U
Semilattices, Finite semilattices. r$ z0 `3 [3 A1 p7 q; \7 D. b x
Semilattices with identity, Finite semilattices with identity8 K( v! \% Q/ h' a( k4 Z
Semilattices with zero
2 N! V0 P/ `2 X! F p) g" N$ VSemirings( u- ~5 n! ?1 H% h( ~, ^! R2 Z
Semirings with identity
' c8 i z( E/ ^Semirings with identity and zero; R7 v ]- Z! r+ P) @
Semirings with zero/ q6 z O" M( X1 @ Y6 b, g
Sequential algebras; @3 z$ x7 P G0 X( j* _
Sets
: C i. Q0 H" ]; xShells4 i5 J9 f' _# `2 q: C8 j
Skew-fields
) ?& ]2 n( P1 t1 H6 ?& V, b5 C/ v1 fSkew_lattices Y" \. l2 Z, F# b8 ~
Small categories, v1 l6 x" |( G; k5 t7 p
Sober T0-spaces2 k) q: W- i5 l; |$ j
Solvable groups, g t' k$ |0 z$ w- {) Z( U
Sqrt-quasi-MV-algebras
+ _! t# V" `# j" P+ E9 j1 fStably compact spaces' }7 G5 p1 W. }
Steiner quasigroups
1 j ~' A* c8 q# q c6 c0 WStone algebras
. t3 D+ r T7 E* j6 ~Symmetric relations2 g* P. I0 f) K+ j$ b. C7 y, ?
T0-spaces( s/ \* _+ S" [- O0 B# z0 |# m
T1-spaces: C- E* ]' S c2 J: \6 W. ]8 |, U
T2-spaces
. b/ z% V# z$ s$ l+ T- BTarski algebras: ?1 E: S7 M- t2 S) Y
Tense algebras
8 v, x3 B7 T* U' o- U5 Z; ], ZTemporal algebras; }8 a1 f" } Q8 M, \# N
Topological groups
7 z& [; Z+ Q" n3 OTopological spaces2 k( V/ M' o2 Z2 W; F
Topological vector spaces
r4 ]. E3 q/ a+ J2 \7 g) oTorsion groups; u# x% d! i/ P+ \# S4 _9 N
Totally ordered abelian groups
6 Q* R/ C( H0 w% r: e$ t+ fTotally ordered groups! e6 X" }; l& ~ }" \2 ~& i& f
Totally ordered monoids' z# `+ B8 [! x3 `, |# [
Transitive relations
" K( t7 p1 `) ^7 \0 o2 qTrees. e9 E+ O9 Q7 }& J. t( s" v
Tournaments
0 k, i3 w8 k$ o+ IUnary algebras! k/ T7 @. P, p( P" p f" C; V
Unique factorization domains/ t5 H$ R3 P3 J9 G
Unital rings/ R7 P- ^' P' p* ~2 ~* m
Vector spaces
5 h" C/ P; B) oWajsberg algebras
! U6 d: L' v9 _( B% LWajsberg hoops
7 h8 d/ n! ^5 S5 G X; IWeakly associative lattices
; F( D, V6 E+ w1 _Weakly associative relation algebras: {, G7 X+ s3 Y% R/ x
Weakly representable relation algebras
( ~4 o2 Q) d% Q. s' a9 q4 g$ s3 e |
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