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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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. T6 l' O% @6 \; M' U) o/ L( z5 ?/ o0 d( H
Abelian groups Abelian group
! |% W( i& b/ Z5 g9 wAbelian lattice-ordered groups
: |$ m6 B% g+ P4 N$ x. QAbelian ordered groups; ]" j2 H+ `. f
Abelian p-groups
3 s$ Q% K: n+ z4 p' @( w4 oAbelian partially ordered groups
% r% g7 G% a7 v: ?7 g |! MAction algebras Action algebra& S4 }- k" U3 c2 T' y6 i
Action lattices* A( t' J5 h: t, f) m
Algebraic lattices. ^( `) E1 V/ A/ r4 [1 o
Algebraic posets Algebraic poset# ?, k% G, s1 L0 i6 L7 n
Algebraic semilattices- V/ S) a) c0 L y$ H( a
Allegories Allegory (category theory), a. H" @# j% r Q+ Y' s, {
Almost distributive lattices* I0 |0 H3 A; f8 N) E6 J. b
Associative algebras Associative algebra; ^5 |" m* A( o% ]: k; ?# H
Banach spaces Banach space9 B v, |7 s l0 S% d& ]" @0 V: \7 e
Bands Band (mathematics), Finite bands
+ k, }$ Y5 E6 d0 l4 K' u+ I HBasic logic algebras- Q m" S4 l8 Q+ L
BCI-algebras BCI algebra
& H% l! C( N# gBCK-algebras BCK algebra
# O. v7 F& v0 SBCK-join-semilattices( B* \8 v& ^: R/ V: o& `
BCK-lattices
3 t1 _$ J1 x j% L) vBCK-meet-semilattices
, L& ]& {) \/ v* IBilinear algebras8 @$ u; O: c% i, N d" n
BL-algebras
; k; W% {. T; F) F/ s& [3 \' i0 \$ ~Binars, Finite binars, with identity, with zero, with identity and zero,
0 D# a$ }& `4 ^1 ]) U" sBoolean algebras Boolean algebra (structure)
$ \ S9 C" ?- pBoolean algebras with operators; t: c& Z& f; j: ~% U7 X9 n2 w
Boolean groups
+ o6 O; e+ ]8 x1 J2 J- b3 w, rBoolean lattices
2 y1 h; s: @" } l+ T1 @0 FBoolean modules over a relation algebra- p8 v. Z: E. z d; b7 c: ^
Boolean monoids
+ [+ e) e. U" O) }. S4 QBoolean rings
' N% \5 H9 C6 E- DBoolean semigroups; B8 p# q; ^# W# \/ X
Boolean semilattices
3 J8 z, R) R" Y p/ X4 s" {4 V: NBoolean spaces0 e3 W: ^5 H7 R
Bounded distributive lattices+ Y7 }+ L" B' B2 I
Bounded lattices
# m8 [( C3 ?9 N+ | G8 U# e3 ZBounded residuated lattices
' p0 r& i: {6 t1 t# Q% V( \2 sBrouwerian algebras
' A7 V/ ]7 x1 n. kBrouwerian semilattices" |* w; [/ p& P- f/ n
C*-algebras( _! g' G5 j' D, U0 y! H+ K
Cancellative commutative monoids
$ \' e- `4 |! j2 k. t5 t8 Q+ RCancellative commutative semigroups, i9 Y* e+ ^5 ^. }( j$ _
Cancellative monoids
; K' E, r5 y. B( h, oCancellative semigroups
& q0 ^( C: m Q" L; h+ tCancellative residuated lattices
- \/ ?" D2 V* rCategories
3 i8 o* \# ]8 d3 L J t2 JChains
4 z1 R" t7 R* x- L u( Z7 x+ ]Clifford semigroups, L) l5 R7 D# L
Clifford algebras
1 A4 D, N. q6 w6 B6 \Closure algebras
( o8 P6 y, h1 q' O9 U7 A- hCommutative BCK-algebras
3 m" {3 X2 X0 E% }; |. W% GCommutative binars, Finite commutative binars, with identity, with zero, with identity and zero
' V. f) a' E( S% Ccommutative integral ordered monoids, finite commutative integral ordered monoids j% n& q& |+ x! v0 ~( O
Commutative inverse semigroups
: N& k1 h7 a2 jCommutative lattice-ordered monoids
* ~! I+ a6 G6 \% u, U, nCommutative lattice-ordered rings1 X, {2 U A$ e
Commutative lattice-ordered semigroups
$ S1 l0 l+ b4 o5 H) |Commutative monoids, Finite commutative monoids, Finite commutative monoids with zero
6 h+ i+ H0 A1 b* F* ICommutative ordered monoids+ K+ ^: c! t6 ?" K2 w6 r' U) l
Commutative ordered rings
. k! i1 Q% k5 Z* v- rCommutative ordered semigroups, Finite commutative ordered semigroups
8 N/ H2 l# k6 b; [4 d- jCommutative partially ordered monoids
4 u# \- l F7 m L& o) q8 ZCommutative partially ordered semigroups
X; C6 u, w# F/ {( P1 L8 dCommutative regular rings
9 I7 q/ S6 q; ~) E+ A5 zCommutative residuated lattice-ordered semigroups0 f9 B! U3 p% G2 k3 M
Commutative residuated lattices
+ @" v' R+ u2 L5 g% B8 SCommutative residuated partially ordered monoids" \* a+ V4 b8 r0 z
Commutative residuated partially ordered semigroups$ C0 b7 E8 g. H/ r
Commutative rings
2 l% K. M2 H @1 ?! yCommutative rings with identity
7 j- p( ]1 K( Q+ C* D: k) ICommutative semigroups, Finite commutative semigroups, with zero+ E( t8 i( B& l$ g1 E
Compact topological spaces
% m( S7 v+ o. A! L4 ECompact zero-dimensional Hausdorff spaces
% E+ X* X: h% uComplemented lattices
% D6 W1 c- D) e( W6 M' FComplemented distributive lattices
# n# W) J( z! s, r# GComplemented modular lattices7 c9 s( E2 |0 t) a7 u4 O
Complete distributive lattices* s& s' z& c$ N& K8 R. h
Complete lattices
0 _; H1 s, C$ F# `1 D# m O. }8 @Complete semilattices; @6 x) e E! Z0 f
Complete partial orders' V8 m$ C* \% q7 q3 K
Completely regular Hausdorff spaces3 p% R1 B V/ V/ `( A' V! k
Completely regular semigroups) ?5 _8 O/ X$ C9 j( G
Continuous lattices
% L8 X7 B& q4 e. c' ^& A5 OContinuous posets
0 Q# j+ H4 p/ N8 tCylindric algebras! R0 e" l4 ~! T }
De Morgan algebras) S+ I: H* C1 B$ _7 l% ?' F
De Morgan monoids
) p7 j) ^) u0 }' s* k& mDedekind categories' N$ g+ J2 I3 X0 y
Dedekind domains
0 @: g5 P1 h' ^+ ZDense linear orders8 x* s7 b# B0 U* |2 S
Digraph algebras
, r( U. w6 C, S% m, c' R$ ZDirected complete partial orders5 f* a- b$ k; D/ O8 B2 {3 l
Directed partial orders
' n4 b3 ?/ ~: H: O6 d$ g) iDirected graphs
/ m* G! ]. u* a' X8 Y; O/ oDirectoids( V% M& B1 T+ g( W9 Q Y% X
Distributive allegories
4 ^% z. ^ d6 E% uDistributive double p-algebras
/ ?% y0 R/ q+ D( sDistributive dual p-algebras
. Y7 E1 a$ A/ A2 y- w" ?Distributive lattice expansions( S3 a( t7 L) S7 N M( x0 o
Distributive lattices2 b+ S5 w( w+ x0 f6 U. [
Distributive lattices with operators* o# q. f' l6 b J/ T
Distributive lattice ordered semigroups* u+ M/ j- B5 n$ {; {7 S
Distributive p-algebras# [5 ?, |7 c M6 p/ X9 |
Distributive residuated lattices
9 x0 A( i. q. j6 ADivision algebras P7 x" Z. F4 J$ z x- e m5 k
Division rings
# D% L0 L# a" G1 }Double Stone algebras
' t( M7 M J% o6 `2 TDunn monoids/ Q' K9 K1 C5 T+ D6 T0 s/ b
Dynamic algebras% {4 v* C, \9 G
Entropic groupoids
5 p$ F8 u! Q( @' O/ oEquivalence algebras
! v; A8 D9 s8 k9 S8 ?Equivalence relations
5 T% K% [9 [; X8 CEuclidean domains7 r) H. V1 v$ D
f-rings0 ]/ h6 r$ K6 T* D+ x9 K0 |0 z
Fields; U/ E% A) f; l2 X. q8 M
FL-algebras5 D9 }: S! I5 }7 p. ~. t: o
FLc-algebras3 l/ y- e9 `0 T" y
FLe-algebras
5 T$ O2 {1 O% T! h DFLew-algebras" z0 Y. K1 Z! m5 D# K
FLw-algebras/ S* l8 I" P# y2 n/ e
Frames3 ?; b( z6 t# ^9 U% O: ?
Function rings
9 c: [- F/ x- d I6 ]* o- pG-sets
* G5 g# p: p& z5 B5 Q4 uGeneralized BL-algebras K* z# G- @ J$ v! I
Generalized Boolean algebras. g/ w; M2 ^( p) [+ m; k% a
Generalized MV-algebras* o( B/ v4 X6 R9 w; v" C
Goedel algebras9 r; t. b7 i5 |8 ^
Graphs
9 y) V& u/ h) _; EGroupoids9 d& f: m2 e' v& ?3 L3 S
Groups$ F5 C# C) }2 N1 q: p
Hausdorff spaces$ p$ A5 R' T' z$ ]
Heyting algebras
* K9 b! V6 ?; h0 NHilbert algebras
: A0 d3 A7 H! F, p4 |6 r" ^Hilbert spaces' q, j, u5 s9 Z9 ]4 J( o- a
Hoops4 X/ @& A8 w$ B
Idempotent semirings
/ U% C0 ?( ]: J( l- W8 d% hIdempotent semirings with identity
" ^$ }5 s8 a: G. mIdempotent semirings with identity and zero2 V( `& o3 O: m. [" S4 O/ s+ `5 ^
Idempotent semirings with zero
( p) X# e" O6 OImplication algebras) Q1 Y5 U3 V0 M3 q2 d
Implicative lattices1 {; b: i; @ y. b+ [9 q
Integral domains
$ [4 @. C3 h+ v' J# ?* |Integral ordered monoids, finite integral ordered monoids" S& h6 O' O; y& \7 Y' k
Integral relation algebras
0 \; i8 Y! j; ?) \Integral residuated lattices6 Z) L) z. ?; E
Intuitionistic linear logic algebras
# I0 b' j4 f3 e; s4 sInverse semigroups: N4 P& p P& l
Involutive lattices
5 J1 a7 f9 n* V' q9 u' D/ aInvolutive residuated lattices* T2 t, W! c/ e5 c
Join-semidistributive lattices
1 C+ Z8 e3 }7 c6 _5 UJoin-semilattices
# v: `6 D% u4 ]5 z9 E" wJordan algebras
# ?& H. V+ v! F- U1 U& d/ T4 I9 |Kleene algebras
" g5 k+ f: x4 C, LKleene lattices0 U' h8 J: I8 e- `& P5 ^; ^
Lambek algebras- q1 W. `' `/ A+ l6 [/ S* w% Y6 |" n. w
Lattice-ordered groups
& i9 P* J, I5 g1 Y. F5 Q% A6 PLattice-ordered monoids
" z) W2 `' ]( C8 ~( ?' U0 rLattice-ordered rings
2 ?$ P+ Z1 J8 r' K' kLattice-ordered semigroups ^# [+ z, q: q0 h3 b0 F
Lattices
5 B8 e8 R* }6 ?0 f$ LLeft cancellative semigroups
9 w" u5 y0 w/ f3 w/ S3 b$ LLie algebras; v3 J7 x6 Z' W; G6 G, \+ D X8 I
Linear Heyting algebras
5 r! k+ j' x8 G z k% ~4 ULinear logic algebras$ T8 A+ O- S+ `' v* ^; n
Linear orders$ l* p3 V; E) H% R2 R
Locales
) U1 H( X- A3 MLocally compact topological spaces
( t8 v5 t+ y2 A* KLoops9 d( \( d6 W1 @
Lukasiewicz algebras of order n/ r: M. `" x: |- W. s
M-sets
- y3 W" d9 J; d# x" g' t" O. {Medial groupoids# H& K0 U8 `8 \" T
Medial quasigroups
1 X6 L& G3 v, a. Q4 m# LMeet-semidistributive lattices7 S# Z# H2 E; F1 W0 j. ~7 X+ E
Meet-semilattices' a& Z3 C0 l3 s% ?: l* i
Metric spaces3 g1 w4 l/ l2 Z% e8 Q; R0 N4 i) l9 y
Modal algebras
6 ^1 ^( c2 J& H NModular lattices
' O9 H) H5 w1 |% qModular ortholattices
0 x0 K4 i9 l6 e% q5 M5 K, TModules over a ring
4 Y. P2 K: U5 z4 \& mMonadic algebras0 ]% O& h4 M8 Y6 ^4 m7 _; b
Monoidal t-norm logic algebras
% d+ b# F8 E0 s: h) ?Monoids, Finite monoids, with zero# f6 L/ l( g! K$ G0 U
Moufang loops
' Z0 I1 K& T2 o; d: [) _0 e( P, mMoufang quasigroups
0 f6 z# \+ A8 T7 J' Z+ |Multiplicative additive linear logic algebras
& H9 T) m+ B J! U BMultiplicative lattices
/ g4 Q; z- e0 w; D" gMultiplicative semilattices: X; }( d4 v. b/ i2 G. P
Multisets
& D! K( W6 \- D8 H. p5 o; \MV-algebras
( s% F- m% V- E; `% y( ANeardistributive lattices
" s; J W- t+ HNear-rings3 O7 a2 D/ X& S) G" D
Near-rings with identity
7 H/ w# I) i& ?* cNear-fields5 T# G7 {" X/ a
Nilpotent groups7 }* I" g: B, x5 U# L5 B
Nonassociative relation algebras$ ?7 ]* Q! Q* [! x9 h. Z5 X% T3 m5 W
Nonassociative algebras+ n% [& v2 }8 E% ]" W
Normal bands$ ^0 l; ^) l1 J- W9 ]/ u; W7 B# D
Normal valued lattice-ordered groups
8 u6 k) J, Z' T' I2 ONormed vector spaces" l! l3 T, r7 q- e
Ockham algebras
# L. p$ s0 a1 ^' ~Order algebras
1 r6 ` D# t! n) r2 @& S* _; mOrdered abelian groups, C- V: V; U( n$ n
Ordered fields
A5 I- r) a8 L* hOrdered groups* M' v; M8 Q3 V1 h
Ordered monoids
4 u6 ~. o0 l# ^ YOrdered monoids with zero
/ U0 ^0 a3 v8 ^" UOrdered rings
6 l0 L/ W1 a; A- M; w1 n. }Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero
* w$ Q4 O9 r: G& aOrdered semilattices, Finite ordered semilattices
8 r3 |: L4 A8 j, ]' AOrdered sets
1 @9 B2 B+ f2 y. w9 M: uOre domains) A$ {, R* w' G* n& M, F8 l
Ortholattices
6 m4 Y4 ~0 J8 S( F2 JOrthomodular lattices- \# r1 P* j+ Q' o- L1 p' y
p-groups) @2 A5 e* @) q8 E5 U6 V e
Partial groupoids/ {* D" ^6 X; o R% E( m
Partial semigroups
, `* f K8 c, R' x& s1 ?. z9 ]Partially ordered groups3 L. V/ b9 R9 k- H# a
Partially ordered monoids
7 ?; z1 t/ \' G2 C3 sPartially ordered semigroups0 I3 j* m4 [5 ]4 J2 W8 C9 |
Partially ordered sets( E( @6 K" F4 E$ ]7 |9 t
Peirce algebras
7 j1 R1 ^ \4 f& o" I! @# D- @Pocrims% t" \ x2 F L; F0 ]$ M
Pointed residuated lattices
d' W# I$ e. T* ~" N! ]" W* gPolrims y* J5 h0 N3 E$ d% m% x
Polyadic algebras
6 Y* E9 M% b9 j: y( q+ M9 G" tPosets
* B c, T: x+ A4 k8 p5 ]Post algebras
# \% p$ h. v f* k" h2 E1 BPreordered sets
6 ~: V' c4 [' r2 k. l$ c- MPriestley spaces
( _' z: M/ _; `6 ^Principal Ideal Domains) D5 B# X+ j* \: z
Process algebras0 k' l3 ]9 Z+ X
Pseudo basic logic algebras
& m: W4 Y2 L1 @Pseudo MTL-algebras7 M' c( b& _ g5 K
Pseudo MV-algebras( ]5 f- u& S' _6 ^' x, o( G
Pseudocomplemented distributive lattices9 `8 R( i- J- V( s
Pure discriminator algebras
# g$ A# R8 g# d9 O9 l6 S& q* s( [3 f. IQuantales5 N$ y7 X2 X3 A7 }
Quasigroups; h6 g* O- i" R7 r1 R
Quasi-implication algebras! @4 [; ^. r6 }" F; h' x" x+ m" Z
Quasi-MV-algebra! D, {) c/ D$ C |
Quasi-ordered sets
, W# w8 A7 F8 }/ Q g b2 I! qQuasitrivial groupoids
* P2 j+ J+ Y m, cRectangular bands
* ]& g4 s. J L$ dReflexive relations% J2 J; T9 |; v4 B& W& ^! R8 `/ T! _
Regular rings5 N" V) C0 m* ~: E9 L, g7 n5 |: t
Regular semigroups4 s+ d! k' B& [, |
Relation algebras
1 U- F" M6 L# A: q8 O5 t9 @. zRelative Stone algebras' D% s- b+ A! B" X+ Z+ r3 ^
Relativized relation algebras
/ P- v8 j# p' ?8 Q- C9 R* CRepresentable cylindric algebras
% {. J* @& q8 G5 O+ g! X7 U3 MRepresentable lattice-ordered groups$ i w0 x4 S8 D* w- ]0 V
Representable relation algebras% V7 V a* g( F# B8 p/ M, m! S
Representable residuated lattices- b$ X# ~: g# F; |! C R
Residuated idempotent semirings1 H0 L2 H+ q9 U, v1 o2 P
Residuated lattice-ordered semigroups" o w" F# h, o. ?
Residuated lattices) I+ u: k; y+ B5 t( x0 j
Residuated partially ordered monoids" @! \* s( r* K, p
Residuated partially ordered semigroups1 [# g7 y1 t( s! d( j0 N+ ~5 l
Rings
! w1 V' E. j, x5 T& sRings with identity
, \7 r: j; f+ }: F# q9 OSchroeder categories3 W3 D) I" M! _5 {; ]) j5 Q1 K( m
Semiassociative relation algebras
P, _5 W: \$ q+ jSemidistributive lattices
3 e, H$ N+ i5 jSemigroups, Finite semigroups
" W$ |) f+ j1 Y9 f5 A7 gSemigroups with identity4 f# Q5 ^5 b3 [7 [ K; \% Z
Semigroups with zero, Finite semigroups with zero
( h. q9 I5 I: j" V: X4 zSemilattices, Finite semilattices
5 z% ^: l/ W' [4 w' G Q1 l aSemilattices with identity, Finite semilattices with identity* \* V N" \& @& t
Semilattices with zero
( `# w! f0 h+ t3 wSemirings
; Q4 T% A* R2 _ W% v4 MSemirings with identity
( {( r7 n" R- [* Z9 j2 WSemirings with identity and zero2 Y8 S& |% h4 k$ g8 D
Semirings with zero
6 ]& f! t. k2 y8 A) ~. GSequential algebras l7 i E/ x0 D# v/ t" u
Sets" }6 N% ? X; c, d! F, V/ }5 Y" a
Shells
: e9 j: i0 ^# H# i) _( f% }" ?Skew-fields
6 r) i" z4 q5 BSkew_lattices. G# G4 f' L( l7 U8 M
Small categories+ [# N- s% J- [; Q$ \9 a
Sober T0-spaces
6 d& ^6 G! c3 hSolvable groups% N' V2 e4 T g% p3 W n
Sqrt-quasi-MV-algebras
7 n$ s5 C% k' l# o6 NStably compact spaces
* U. N/ ?; T: r% l; iSteiner quasigroups
$ X$ Z+ y- G" j) HStone algebras; b/ \; h: S; x: D# u9 [0 h
Symmetric relations
1 Y. y6 Q1 z9 _# `6 \# UT0-spaces: m. L+ r- j, Q! f4 X+ p1 w N9 Y
T1-spaces
% r9 R. c$ ~) T# R. p: a. dT2-spaces
! z* u" J. c8 K1 D1 u. JTarski algebras' @$ j: f; x; {7 Z
Tense algebras
) f# }; ?, `+ N' |$ B3 aTemporal algebras- \1 K. N" h1 |8 S1 v0 M% n# ~
Topological groups
" k/ B7 p$ B$ p3 @: RTopological spaces
/ A8 p V% r: z2 l Z" |# ETopological vector spaces4 x9 g& o; ?1 }
Torsion groups
" {' i& f" c4 s- K ^5 {3 Y8 Z- DTotally ordered abelian groups1 Y" N( |7 @; M, V1 M# C
Totally ordered groups" S. L% m/ G( w: n- l h
Totally ordered monoids
- y* K' q9 e& Y1 pTransitive relations8 p* d# M5 ~1 _* B* @% j2 I
Trees, l: Y7 ^! O: B5 z d. K# e
Tournaments9 a" D4 Z- V* W. V1 _" L: P2 v; \
Unary algebras
$ u* o$ w" V% D. z" J8 \" sUnique factorization domains
7 c: @2 }: `% H. y9 ?: ^" ]5 L; Z8 ^Unital rings1 \5 M7 S# q' s
Vector spaces
# O' j- _& |+ N# C7 L1 ^9 CWajsberg algebras; D* z5 d I5 j3 I$ z, ^: v
Wajsberg hoops
) R8 a9 C. l7 K1 L1 TWeakly associative lattices* q0 E9 Z. Q2 _, r" ^. a% C7 X
Weakly associative relation algebras! d S. T# f/ {% m/ j2 M8 H- K/ H
Weakly representable relation algebras
/ W1 r1 J- C* ]3 i |
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