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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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6 h. J9 p# W0 ?1 z0 r+ F% V0 e- X% P
* v/ Z" O4 f5 K8 j0 }0 c2 {Abelian groups Abelian group
2 H8 R2 n, s3 Z# T3 z# ^% Y" MAbelian lattice-ordered groups
" v' O; B$ b5 o3 v! v3 K# k1 [Abelian ordered groups
9 k8 m4 i/ Y' E% `$ z. Z. P2 \; ]Abelian p-groups
6 z" N% j) x! Z, o% T, FAbelian partially ordered groups0 |% V2 H* d$ I, ^9 ^
Action algebras Action algebra* n1 _, e" p( t: {5 \
Action lattices8 U ^" r' \* P' g$ [
Algebraic lattices! K8 s5 R" Q" t& q8 s
Algebraic posets Algebraic poset1 L1 N% t& m+ G+ \9 V
Algebraic semilattices& y# N& i- c% z1 [( G# \0 Z9 Q
Allegories Allegory (category theory)
" v; e, T: d0 ~. tAlmost distributive lattices
) t) H# D/ ?% s0 G- L/ ^" K' DAssociative algebras Associative algebra
7 V5 q- ~6 X" w9 K6 ^+ U; HBanach spaces Banach space
8 j, c% ~7 o+ B% ]% XBands Band (mathematics), Finite bands- z6 x+ x, n5 s- }7 e; i
Basic logic algebras
3 k7 T9 M6 Z) Y: v5 P; qBCI-algebras BCI algebra
1 X& Y) |! T- @; ]9 k gBCK-algebras BCK algebra
9 ^ j/ @( W) ^3 b7 n" lBCK-join-semilattices2 m; H! H5 \; P4 V" U1 U9 z* a
BCK-lattices
9 X4 q9 j0 d: lBCK-meet-semilattices
5 a1 S8 N* K3 t( dBilinear algebras
% P1 y: O- B+ ~. E5 QBL-algebras
0 p1 H# ~+ N4 S( uBinars, Finite binars, with identity, with zero, with identity and zero, $ l) u" j; M: M1 C3 o
Boolean algebras Boolean algebra (structure)
j# x7 O3 y$ f+ B8 l: QBoolean algebras with operators
7 d% k+ G% a& V, j9 \8 Z7 gBoolean groups
+ B; T. s9 q" l3 wBoolean lattices! i. b1 ~0 i, I' ]4 z, ?* L" {
Boolean modules over a relation algebra( q; L# ?" x }2 C5 P; N4 o# ^1 i
Boolean monoids
g) J$ c( Z2 i6 X% _Boolean rings. x& ~" G- ?9 G
Boolean semigroups4 O9 \ | t7 Q+ k0 e; m( ? v0 r
Boolean semilattices2 h8 B8 D, v" [) {( |* V% ?
Boolean spaces7 O l C" s" n2 _- c
Bounded distributive lattices9 _& ~: a; T: c3 e; g
Bounded lattices
- Z2 s( X. ]# h; R" vBounded residuated lattices
3 ] H5 [' p3 t9 x! ]Brouwerian algebras8 \" w- f, W; l7 ~1 _
Brouwerian semilattices% R$ o& d/ y. {/ w" r
C*-algebras* u/ l9 F% B# x
Cancellative commutative monoids
3 j4 g, O2 A! k3 }- A4 }Cancellative commutative semigroups5 ]8 q/ R0 ^# |6 n. k
Cancellative monoids" R# P Z2 B$ \1 _% Z4 |0 v' V1 D5 N
Cancellative semigroups
: Y$ h0 @7 X9 b* yCancellative residuated lattices
9 ^( f* | I) Z8 [" P% l2 G4 HCategories: a5 ^/ Z7 k) z' Y" p# K' o
Chains
9 F' G- ^8 D. U+ j+ \+ X6 PClifford semigroups
( e: g6 V4 D/ k) [1 v% S& LClifford algebras
9 Y1 w8 g' E5 u8 n0 MClosure algebras1 f. \" O0 X! d3 |/ X4 d7 B
Commutative BCK-algebras
: c7 B( A$ ]5 Y# u* k' A6 H# f" nCommutative binars, Finite commutative binars, with identity, with zero, with identity and zero
7 U$ F$ p+ I. F7 ?8 u4 Qcommutative integral ordered monoids, finite commutative integral ordered monoids
& e e- V& |. V$ c2 QCommutative inverse semigroups1 ?6 ?& V& {! q5 M
Commutative lattice-ordered monoids
, V8 \' n. J# o5 D0 B2 wCommutative lattice-ordered rings
+ K5 X0 Q$ f! V+ R3 A0 jCommutative lattice-ordered semigroups
9 @( y; c; h: m' D1 q0 oCommutative monoids, Finite commutative monoids, Finite commutative monoids with zero
+ O7 ~" u3 i5 c' H4 uCommutative ordered monoids
% {7 l8 t- D; a2 W8 m( F, \% ]* y% pCommutative ordered rings1 h! V9 }1 ]" X2 t2 o
Commutative ordered semigroups, Finite commutative ordered semigroups
4 m. {( H# g% E- X2 _ D/ lCommutative partially ordered monoids8 Y, L6 @5 Z3 a
Commutative partially ordered semigroups d, R5 X; W) M5 n# K! t; _
Commutative regular rings& B1 ^8 s7 q# j7 ~8 Y0 C8 N
Commutative residuated lattice-ordered semigroups
3 F0 z# a/ D5 h& M# v8 m0 mCommutative residuated lattices Z' t0 z! M' ]3 c9 S" Z( ?
Commutative residuated partially ordered monoids! i4 w# ^) |# }0 g9 p
Commutative residuated partially ordered semigroups2 z+ k/ `4 v+ v2 s
Commutative rings! d n. l7 b \: `' y
Commutative rings with identity- o+ R$ H$ P$ [3 C
Commutative semigroups, Finite commutative semigroups, with zero
- ^' b1 b4 T2 `0 HCompact topological spaces
/ L7 V. ^: A" e6 OCompact zero-dimensional Hausdorff spaces. f% A: n- i; W; D. }! k
Complemented lattices
9 t* w8 F& d4 n0 l3 y' WComplemented distributive lattices
1 }5 f8 G6 a8 v& _% {Complemented modular lattices) {8 y Y3 N" X) Q6 _$ I
Complete distributive lattices4 ], O0 a. x/ f. Z
Complete lattices6 ]+ x2 t* ]2 n
Complete semilattices
& p; f7 _9 l+ g/ c" [8 ~Complete partial orders
( C% J/ \ R0 \: N2 X8 H8 [Completely regular Hausdorff spaces
8 ~. w2 V' w7 x2 S. tCompletely regular semigroups
7 y& t8 p+ {4 wContinuous lattices% H7 E" h! Q& Q L4 U
Continuous posets
% y' P: M) s/ k+ t+ SCylindric algebras1 U6 o; E7 I% s- }' v
De Morgan algebras7 p+ @. {% b3 x
De Morgan monoids! B! H7 E+ K; B$ G! v, d; T, z
Dedekind categories3 h& q4 J" a# M0 {1 ?2 A6 d4 @0 ^! G
Dedekind domains
& r, p, j+ o3 B+ QDense linear orders
5 R3 z2 Z# e% s( R8 Q, D5 E9 mDigraph algebras
! G+ |9 C$ d; L) X; bDirected complete partial orders0 ^1 B" i3 A, N" h: h! a
Directed partial orders1 G D" G4 G( V& W1 ]- M- u
Directed graphs# P4 ?% r6 ]5 s8 x* W1 R* Y
Directoids
! c" z+ ]1 V/ o% C oDistributive allegories. C/ T3 H( F# |
Distributive double p-algebras( u6 g2 j0 X4 c$ m
Distributive dual p-algebras% Z7 ]- L% x* A8 p$ J
Distributive lattice expansions
9 u; S0 Z1 j9 [7 K- GDistributive lattices
% e+ T6 a3 J9 dDistributive lattices with operators
: v# S0 D6 t5 T' d: d! D% hDistributive lattice ordered semigroups
, `% {+ V$ i8 U$ J9 e: FDistributive p-algebras
; T. Z: e/ @* Q7 X+ p" rDistributive residuated lattices3 S7 E$ Z, N. \; W8 |; V( f
Division algebras5 Q% V7 |5 C. E$ o" d* n
Division rings# @" X& S( |( ], F
Double Stone algebras' W6 R& w( o9 N! k* E9 W
Dunn monoids; V% u3 l5 a( V- ^2 C6 m c
Dynamic algebras
8 q, d' l0 t- h/ q: [$ \" o) CEntropic groupoids
, }8 J7 f7 b, z2 l9 e' u }Equivalence algebras. ~0 A+ o- {3 F& ~( D/ |
Equivalence relations% T `7 Q9 B) u4 }
Euclidean domains% G1 |3 t0 n, `# n
f-rings
" y ^$ x( l: Y* @1 hFields- U/ I) h, C' y6 P% p Y/ J/ t
FL-algebras
5 E; s5 X7 `. {# y0 iFLc-algebras
7 F4 C# x, G6 v5 ^8 n) GFLe-algebras+ J! Y( G( ` w5 A+ C
FLew-algebras
& z$ M/ T2 ]& l7 q1 dFLw-algebras
m* Q. I- z" l; `3 C; @Frames
' p+ ?4 g2 J, O' L3 s" hFunction rings% U; `! _, h6 c7 M% |! O, [" E& F
G-sets* V. s \; Y% p) U. g
Generalized BL-algebras
1 d5 n, ^& t* ^7 z- uGeneralized Boolean algebras) r' K3 L3 Z+ l* d
Generalized MV-algebras
0 z2 f O. f7 j7 T2 oGoedel algebras
8 f. c4 ~2 b! [$ F% w8 rGraphs
# M9 ~: I. |, M3 M7 V6 fGroupoids+ ]2 K! i; ~& s8 c
Groups
7 D, C; N5 R: {% IHausdorff spaces' G. B0 F$ E- ^6 a
Heyting algebras' D+ F/ O& D0 b. S/ E" U
Hilbert algebras: V3 F9 O; J& O- ?8 F" ?( c
Hilbert spaces
7 O0 @/ k: ^+ S% }9 nHoops
) k; x) `+ G% ^- _Idempotent semirings
) V, ?# Y( h7 I. D2 o7 JIdempotent semirings with identity& R" p% Y+ g8 n- e
Idempotent semirings with identity and zero4 }* r* [$ k2 }) `3 z( h# P
Idempotent semirings with zero0 y& F6 R1 x- H' r
Implication algebras
/ Z9 T' J. j0 a' c9 D t* w" r3 iImplicative lattices4 f4 S0 d% ~( k8 l+ k
Integral domains
- f0 e* N8 K* q3 ^- ?Integral ordered monoids, finite integral ordered monoids
9 E' Q0 Y: A+ { HIntegral relation algebras7 L9 V/ n" G5 q7 M( `3 y
Integral residuated lattices
* e% G) w) x& n% `* Q: c nIntuitionistic linear logic algebras
2 w5 b( H I# ~* K1 V+ s6 I3 r1 UInverse semigroups
3 s$ _6 Z9 h5 ~; j% o1 e- mInvolutive lattices; ? J' \8 i! y3 u8 M
Involutive residuated lattices
% E& W0 U& N' S" Z: SJoin-semidistributive lattices9 L# P3 _5 J) y% G
Join-semilattices
* |. ~$ B3 W8 C; e/ S) I. C. PJordan algebras9 x+ k8 V8 m: _; a; V m0 C
Kleene algebras
4 f3 J f( N1 o) J8 S3 @Kleene lattices
0 J% \/ H4 c c; Y" N) RLambek algebras
! r$ n8 L+ ], _# q9 pLattice-ordered groups
6 n' C; J* r+ p# x U8 uLattice-ordered monoids( V; o* a$ g% z* [4 s: v3 v' k
Lattice-ordered rings$ Q$ k; r: Q9 ^. d4 \( H
Lattice-ordered semigroups' r4 e! v" [4 p( K) e( J/ ]
Lattices3 n- K/ G9 d' `
Left cancellative semigroups/ h; G7 }8 W1 v8 X* x
Lie algebras
5 [1 O, K9 T, j6 n0 v# ~Linear Heyting algebras
% C8 _9 ? ~9 R- sLinear logic algebras. b8 f8 B) {, s, y2 D. }
Linear orders
# ?1 S4 [+ v' E) r7 ~% t+ |Locales
0 K/ u7 K; e( }' oLocally compact topological spaces
/ C" z9 T( G& @. u6 wLoops9 T/ h9 G2 a7 u- c. ]
Lukasiewicz algebras of order n
) v/ v/ v' x$ W. wM-sets
, e0 f" Q" h) u/ |* D1 t- T6 xMedial groupoids
1 c6 a: F" A! ~) R% m6 UMedial quasigroups
, }$ S; T' R8 O) h' zMeet-semidistributive lattices
' Q$ J5 Y* {! Y! m8 DMeet-semilattices
1 Z: e9 y) ]8 ]8 ?1 ]% ?: XMetric spaces) I) d' y/ N- c `; y& c
Modal algebras
3 y" [2 x1 G( ?$ j! A2 i9 LModular lattices
9 L V+ `( T/ l& hModular ortholattices
& T0 |! e, M4 W- [Modules over a ring
! O/ [8 U0 m6 o8 cMonadic algebras/ Y4 ^% Q) z+ Z, Y- z. ?. L+ T
Monoidal t-norm logic algebras
5 ]- u+ L3 }) E* j7 @! f2 o; v3 [Monoids, Finite monoids, with zero; `9 e! C+ J! G; N9 o
Moufang loops
& c; y) Z- S0 D7 {Moufang quasigroups
" d6 Q) F7 e, q4 p( H( U) UMultiplicative additive linear logic algebras& `1 }7 e4 [; e4 i
Multiplicative lattices
. d4 q1 @: T( X9 O& f" LMultiplicative semilattices3 B3 j" r- P& p. A) V
Multisets$ \$ ^' p4 Y' E( M7 q2 H4 h$ y
MV-algebras
. K- T3 F! M' gNeardistributive lattices. k6 x/ t, N$ Z; C/ w$ p1 t
Near-rings
; b% e2 V& k, j( r% v* X8 gNear-rings with identity
: I. b! Z) U/ V9 sNear-fields
* ^& d2 T" Y6 K# Z4 dNilpotent groups* V- M6 H. c5 @
Nonassociative relation algebras* j$ H$ J2 S# m
Nonassociative algebras
: g0 `& Q, w- R- X$ |4 B7 y! o2 jNormal bands4 m: V4 W% [ A- C
Normal valued lattice-ordered groups3 |2 H. Q" j! C X6 ?
Normed vector spaces
% j8 U1 ?# \8 l2 e/ C) OOckham algebras
8 J7 u7 n/ ^2 W! M8 iOrder algebras; E. Q+ Q( \3 W: C
Ordered abelian groups7 u6 H0 P: H8 G# E$ v
Ordered fields7 s' s/ O/ b0 p [3 q @6 B
Ordered groups9 g* L; A2 p( ]- A! M- V
Ordered monoids
" y; z/ e2 B# ^2 d/ `" iOrdered monoids with zero. u' u. M$ J, L9 p4 f2 Q/ _& x
Ordered rings
1 J* R1 r ] e x8 IOrdered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero
4 r8 D+ Y2 R+ SOrdered semilattices, Finite ordered semilattices L2 U# J* r" N/ o; @
Ordered sets6 D3 \+ H& p& S/ o$ M' I& b: ]! _
Ore domains; ~0 C/ Z' x; p) d+ d9 T3 H9 _
Ortholattices
1 g3 Q0 _5 b7 M! u- T+ @/ FOrthomodular lattices
$ M$ u7 m3 ?. O r2 yp-groups2 E* g6 X) Q" d$ K& D2 L
Partial groupoids
6 ?# {+ \3 k k) w( I9 y! b vPartial semigroups
( r% X5 { N' \ ]1 IPartially ordered groups
A3 q! b: m0 V) Z- }3 C7 cPartially ordered monoids* G) D% @# P/ u# G2 b: n
Partially ordered semigroups
6 p, W7 j, m! W# g) Z. N ^6 }1 N( nPartially ordered sets n- z" ^8 q ]
Peirce algebras
. i$ u% g- s$ q' y* w7 C+ ?9 uPocrims
$ i) O+ t! a RPointed residuated lattices
! y4 }' |- s+ x, R# RPolrims
0 a( z, \+ ^" |' Y5 }Polyadic algebras
# y/ V! t* k; `0 bPosets
1 v. K2 b5 g5 g) ?# c$ vPost algebras' q6 b! g, K# O7 R, v0 J+ U
Preordered sets L- t& h% m1 H$ { B4 H
Priestley spaces
$ r/ v. T, p; @Principal Ideal Domains+ z: V9 g# V" g$ o8 d& r/ g: ?0 G
Process algebras h/ B; s, Q# c& C1 z
Pseudo basic logic algebras: J" ^- r3 _; M; p* z5 p
Pseudo MTL-algebras1 ]1 y+ Y# x* c: L1 I% q- B8 F6 }
Pseudo MV-algebras; r5 n8 H1 E1 B
Pseudocomplemented distributive lattices
) g6 I# |& |1 q! i2 M' v: _! p1 C- `Pure discriminator algebras
+ _$ r1 y. J2 H3 O% n) ?Quantales
* G$ U4 |+ p D# ~: f2 e. \Quasigroups
5 i' \5 v, h4 h" }2 cQuasi-implication algebras2 z* G( m# d5 G) @1 `" R1 K' @
Quasi-MV-algebra: I6 p ?) [ h$ [
Quasi-ordered sets0 Y7 A/ R3 ]& {$ q. p# |
Quasitrivial groupoids
$ N+ @! J1 W! u. R5 f$ dRectangular bands
( D0 @3 _1 Z( j+ _/ y9 y; F1 NReflexive relations6 p& l6 n7 i5 t* z) q
Regular rings
: z! }$ k l; ?Regular semigroups
; U8 I( c$ R/ t# r2 jRelation algebras
. p, e+ B* P; `8 }* SRelative Stone algebras
}. v5 @/ }4 B! I- yRelativized relation algebras
/ G0 l+ m7 }) x3 yRepresentable cylindric algebras
' m7 B$ S/ J8 R: Z9 E6 U$ kRepresentable lattice-ordered groups& s+ m; h, c6 Q+ B
Representable relation algebras8 k0 m, n% [# R9 Z8 t1 f
Representable residuated lattices; P' g$ A7 a% F6 q; v+ r/ U/ `# n
Residuated idempotent semirings+ c+ I. n" {$ {6 T7 J- g
Residuated lattice-ordered semigroups& A2 Z" o+ A r+ |
Residuated lattices; V) O5 l; Y# s0 a7 R& @( K
Residuated partially ordered monoids$ q' U, k8 L2 F6 C" K6 S+ Z
Residuated partially ordered semigroups
1 B# {) t) c z6 v, r( QRings$ |9 ~+ g0 |* {1 o$ W9 l
Rings with identity
; }$ p; l: C9 d7 t, `. t) FSchroeder categories
' ?9 G2 \! T9 e) H; Z5 i1 x9 n& eSemiassociative relation algebras
& r) B5 j7 s ]- H/ \Semidistributive lattices
- O! q* X6 B A4 c: D( xSemigroups, Finite semigroups
- j) @ ]) e8 R: i* p) |Semigroups with identity7 D' D- t" m* A1 d' T* J' {9 R" T
Semigroups with zero, Finite semigroups with zero' s3 B% s! [( B, j7 @
Semilattices, Finite semilattices/ D1 r+ U3 F2 w" S* e9 Q: O
Semilattices with identity, Finite semilattices with identity
5 g$ c) p4 j, y7 `/ _6 M |Semilattices with zero
( X( s1 \! r/ ?+ @: v" z" \Semirings
$ \8 } I6 m% Z5 T ZSemirings with identity4 M! g; U9 v7 K# I4 d# G
Semirings with identity and zero: K' Y$ i8 O* B0 V5 R8 ~5 Q; d; T0 m
Semirings with zero9 s9 E6 G% U! Z
Sequential algebras
5 B! r) C9 \1 D8 J3 k0 n% lSets
1 E: Z; J: q! x7 O8 O/ \Shells
9 \6 ^6 b. e1 S. [( l, K! }Skew-fields
7 N2 D2 ~$ C6 ^* v9 \! ?Skew_lattices
* r+ t' l7 ~" V' W1 X5 QSmall categories$ g5 Z7 u$ I5 y4 M" m! \1 C: D
Sober T0-spaces! w4 M5 F: X' h5 R* E7 O4 O
Solvable groups) w, m9 J+ T1 U" J
Sqrt-quasi-MV-algebras2 W* z" \9 M$ C+ l7 Z8 `2 ?
Stably compact spaces
- ?6 _, b5 J+ D6 f6 u% M3 RSteiner quasigroups$ [( a5 w$ u) K x
Stone algebras+ c2 S& X. _# ]# u2 a R8 L
Symmetric relations6 t( d$ \. g% ?4 U8 i" A- s
T0-spaces
' J [/ _! ~4 @: t5 K2 B9 \. X- A& R+ }( FT1-spaces8 V% m2 M- O( q
T2-spaces
7 I, a1 z6 ~3 L: uTarski algebras
) T& I9 `) R' W7 b; w6 I% ?) XTense algebras$ R+ G/ j; q: T$ k5 P6 G [) p
Temporal algebras
7 i) H2 }6 _: U; ?+ y: mTopological groups7 C; E* d* o O# [% G n
Topological spaces
* @7 p; n7 E1 `, G$ }- cTopological vector spaces
& ]- v) s1 [! k3 v! u! p3 iTorsion groups
' c B# I2 D6 t/ L: r, M OTotally ordered abelian groups) U: }! S) R, Q, z& U* U$ c
Totally ordered groups
! i1 B2 O! d2 Z; R) `% bTotally ordered monoids
: p* \3 T5 O0 }6 z$ G6 P% f3 ?8 I" ATransitive relations
; E9 U: l# J8 s7 x# x+ l& g( ]Trees) _5 [2 Y( V' p$ A3 ~
Tournaments
[' Z5 W; I+ k, T6 M* jUnary algebras% {9 ]2 @1 Q$ f1 @3 Y) s" _
Unique factorization domains) O9 c$ N$ U5 {' B. i
Unital rings0 V: ?! f& Z$ X! v, i
Vector spaces$ t; i$ s( |* j3 U" w
Wajsberg algebras9 q5 [3 b+ v8 i; m
Wajsberg hoops$ V1 W; v0 r2 ]! ?8 T+ g* P
Weakly associative lattices
( \" X* N, A( i& ?( HWeakly associative relation algebras
$ A/ C3 f* c5 q" F- C" X+ G# v' uWeakly representable relation algebras! g. A/ j2 [6 ^* B- t9 n; v0 g
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