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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 E- I6 x9 ]" _7 J8 _! [
Abelian groups Abelian group% A8 j$ |# |- c, g3 k
Abelian lattice-ordered groups
4 m0 j$ y9 V. t- O4 y0 JAbelian ordered groups
" L- q( c# ^3 C+ J$ [9 QAbelian p-groups
0 o' _% n$ r4 C2 S& d+ T) M9 L0 {Abelian partially ordered groups
( R0 L+ M5 ^9 z, b! r; J5 p% BAction algebras Action algebra
+ o' l1 }. F0 IAction lattices- C1 a1 U$ ~3 D2 O: Y- S
Algebraic lattices
9 c' Q0 o/ C' d4 `! pAlgebraic posets Algebraic poset e. M5 r: p. _" a# j
Algebraic semilattices
% N$ x& ~8 `" S$ uAllegories Allegory (category theory)0 x; U& c/ ^4 P; C3 g
Almost distributive lattices
$ N( t( Y. q5 ` |" w1 bAssociative algebras Associative algebra; d, a+ }& W: I, p C! F
Banach spaces Banach space& n! M9 \1 e2 H
Bands Band (mathematics), Finite bands% S' g2 _2 p+ v
Basic logic algebras
, G5 _8 S) r6 BBCI-algebras BCI algebra
" w' U: M3 m- xBCK-algebras BCK algebra$ O m( `' t$ z; W& b6 f" w
BCK-join-semilattices
( r8 _% v* f ?+ j7 ?BCK-lattices. A) F7 }+ ~ {0 l; J {! Y
BCK-meet-semilattices7 I4 }6 K0 E) h8 a; |* }
Bilinear algebras
2 H% l* Q5 \' O1 H; v3 t, ?& |BL-algebras
8 Y( c) g# A# D* W4 T8 XBinars, Finite binars, with identity, with zero, with identity and zero,
% V# d3 Q* D% T3 w+ rBoolean algebras Boolean algebra (structure)
, a7 m2 {1 z% A. ^7 E) WBoolean algebras with operators# A" D0 k0 c" k; c) {
Boolean groups) \/ K( K$ c/ T
Boolean lattices# K7 o2 G4 @* U
Boolean modules over a relation algebra( l6 K4 l/ ~/ m9 u, M* f l
Boolean monoids" g! X5 M; t% I$ z2 p3 ^. d
Boolean rings
) ], e4 C& G7 K6 C3 D# IBoolean semigroups) b5 m0 E8 }# i/ G# b2 m1 h
Boolean semilattices9 d" Q6 ~1 Z, w2 e
Boolean spaces
* f/ v/ T& H; R& Q, F2 TBounded distributive lattices
9 [2 K" W: a" S$ S* ^% ]2 hBounded lattices
; N/ E. k" { M" _7 eBounded residuated lattices7 k C% R* I$ {/ u' t1 w$ D
Brouwerian algebras9 @, u2 I% O+ b8 h# c$ {3 C4 d
Brouwerian semilattices3 p3 c9 Y. g% j# p. r7 U
C*-algebras
% {. W& a8 B. ]- x% W5 }( ?Cancellative commutative monoids
6 B' {! {6 J8 CCancellative commutative semigroups
. l9 a6 c6 }) B& VCancellative monoids
5 g4 z! z, O# J: S, @& XCancellative semigroups8 B. L, Z3 E# c
Cancellative residuated lattices
& ?. W8 V' ^8 d: c9 U2 oCategories+ ]% d0 {$ v$ v' p
Chains) z) T. F1 W2 j' X% T% V: ]5 s
Clifford semigroups
3 m! L6 q T$ I" \Clifford algebras
6 \: L4 f" \$ W$ CClosure algebras9 _4 _& w1 a) V) \
Commutative BCK-algebras
- l/ X3 F, d: g+ DCommutative binars, Finite commutative binars, with identity, with zero, with identity and zero 3 t( T X6 l2 w/ F5 D
commutative integral ordered monoids, finite commutative integral ordered monoids
. N L7 t; |' P6 K6 r5 U/ d; XCommutative inverse semigroups
0 ]4 ^5 @+ `+ T, b& SCommutative lattice-ordered monoids4 N' l& L$ d, E1 k" d. d* g5 R
Commutative lattice-ordered rings* C- d4 T2 L, f
Commutative lattice-ordered semigroups
* ]! U( N* y& G* r- wCommutative monoids, Finite commutative monoids, Finite commutative monoids with zero; k8 f5 o" y6 P1 b$ @. n. `) v
Commutative ordered monoids. N5 a! E' p6 E% D3 @2 _# K
Commutative ordered rings5 U: Z% ~& S4 w' [& d: V2 a* j+ B
Commutative ordered semigroups, Finite commutative ordered semigroups
5 s) i: Q5 Q. C$ C+ MCommutative partially ordered monoids+ y2 o: U( W3 R
Commutative partially ordered semigroups
# ]+ }/ J! o: m$ U w6 o2 _Commutative regular rings, n( d7 H7 v, i7 `! |! c
Commutative residuated lattice-ordered semigroups
$ r# y/ y4 L& |: k! _ R) l- ~Commutative residuated lattices
* J7 d6 u. B S* LCommutative residuated partially ordered monoids
T3 f3 y5 @, K% a4 p/ y, \Commutative residuated partially ordered semigroups
+ l' q/ f" o3 {* T/ lCommutative rings
1 `) T, S. d7 ~* @ [/ B, I7 [Commutative rings with identity
& G6 G; H G FCommutative semigroups, Finite commutative semigroups, with zero
: V: I0 u5 z3 ]5 G+ y& p0 e# HCompact topological spaces1 R- a5 U x( z+ a/ |
Compact zero-dimensional Hausdorff spaces
" W0 c$ R6 b) S& B7 b; p& ]Complemented lattices
% E0 n4 L: S5 e0 ~3 \Complemented distributive lattices
( f" u' ~: {2 e9 @# U& Q- sComplemented modular lattices: R7 U* v: y8 k2 |4 V7 |
Complete distributive lattices/ { y* j* U/ z* n; ?
Complete lattices
, {0 X( X5 ]' [% sComplete semilattices; L" e# x4 ~% v: s2 T$ C
Complete partial orders4 I6 b: v) N" @& ]( i- X
Completely regular Hausdorff spaces
: t+ X8 C3 ~5 ]0 l B; m& JCompletely regular semigroups
) R0 ]# l1 t, q% Z& `& Z fContinuous lattices# \2 P7 }1 M [' O3 F$ i3 Z8 Q
Continuous posets
* E" o$ k/ T9 I! P4 dCylindric algebras
( u0 L2 a, P- V' kDe Morgan algebras
0 c g8 a% a+ v S$ @; _De Morgan monoids: @, v5 `2 }1 V6 j: ]
Dedekind categories, G3 x p9 b) x( H% R5 o" b8 ~7 h
Dedekind domains
" W1 | ^% b9 b" u3 D" zDense linear orders
( i5 d3 g- |. l* ?3 r A8 NDigraph algebras6 Q% N( F' H! }
Directed complete partial orders
3 v& y( Y+ x5 T: w3 `Directed partial orders
! f b* s/ J' C: \' S9 ZDirected graphs
) K5 k* L) `+ MDirectoids; Q! C7 e: R& o: v" f! W! @! o
Distributive allegories
; J3 o4 f. v" Q G$ D) XDistributive double p-algebras
3 Z' e" |' f2 S# u z% oDistributive dual p-algebras" ^2 P& ?) N. ^5 j7 w' U( L) m
Distributive lattice expansions
. ^; I" G" f5 I7 V# }5 DDistributive lattices
5 C7 @ F' O8 y3 x8 {Distributive lattices with operators% o4 U" T/ _1 b6 i# G
Distributive lattice ordered semigroups
! x. `( q; ~4 u! q- x+ K( J! \Distributive p-algebras: [% \3 K! K% Y+ x* Q0 G1 ?- b
Distributive residuated lattices
9 d$ t" u9 u5 N- XDivision algebras0 v* K- Y+ ]" w7 `" u6 K; y
Division rings( D9 o# z) K4 k) @/ ?+ F8 l3 c0 ~
Double Stone algebras
2 S, l9 S4 y6 Q, y& FDunn monoids
; `( B' g7 Z- W% P" MDynamic algebras
. _: {+ f3 ?9 A" j, t( |" e) |Entropic groupoids
% A5 A1 X7 j& [5 ^Equivalence algebras
/ L/ [4 w. R! G' M! ~( Z0 XEquivalence relations
p W& K9 Q# h: L% gEuclidean domains% a# D6 K3 x9 v4 g8 C
f-rings
. d o) H1 [& y* I0 ]Fields, n4 k+ D' ~6 }5 @0 ]- [7 [) c
FL-algebras
4 K. S$ Z7 ^8 iFLc-algebras
, c$ j0 r8 J, a) |% sFLe-algebras/ p' x$ ^1 F" @: Y6 V; Y
FLew-algebras2 a& ?+ Y$ ?! p- X. ~
FLw-algebras+ f7 P$ q9 a8 `, O
Frames" F9 v' ^- x- v* N Q
Function rings2 `6 U+ V: i: g; G, _
G-sets
# O a5 H8 x: i& HGeneralized BL-algebras8 @/ h. |6 n- i2 q
Generalized Boolean algebras
' \9 a8 ^: l7 G) NGeneralized MV-algebras
- i, C; [; u7 T- P& R& CGoedel algebras' z# Y! ]: S4 i* t
Graphs
1 G' `2 K4 D/ S u' OGroupoids
( |8 `" ^1 u m. v2 c# w: TGroups
5 a5 n' s8 |- ^# _ r: n" T7 d3 \Hausdorff spaces3 m5 F4 P# p( ?; \0 ?
Heyting algebras2 h+ h# C6 I0 M" H2 z/ B
Hilbert algebras
+ ~1 U2 p% O' H) `3 @5 gHilbert spaces1 c) O. {" @0 I6 F: L
Hoops# \/ H1 o' w X+ h# o
Idempotent semirings
" y) f) t* M9 ]% bIdempotent semirings with identity
& y) ?3 n9 Y4 C" N! s' gIdempotent semirings with identity and zero
5 n& N" I f8 ]$ f% {) I2 eIdempotent semirings with zero5 N* n2 J* W) s g8 U
Implication algebras
, I- D1 O( h n5 QImplicative lattices
% n6 L$ `. Z! D( G) `6 E2 `3 qIntegral domains& D- M5 t8 Q$ l2 Y6 i! p3 }. P. b
Integral ordered monoids, finite integral ordered monoids5 d5 D5 a7 r7 ]' W W+ S, R
Integral relation algebras# f5 T$ d3 H. y6 ?/ _
Integral residuated lattices
, M& N, N, f1 M& D* _Intuitionistic linear logic algebras" _3 C( M; ]/ I. Y/ F7 V
Inverse semigroups& N" ?% a1 Z @4 I8 W
Involutive lattices8 B! l3 X D& P+ S1 i3 m, t
Involutive residuated lattices
( n' w5 E6 S1 f; R# P! O9 K1 n r5 ZJoin-semidistributive lattices: C2 Q; S# }! A8 w- Y" M
Join-semilattices
" A- K* |+ a# e2 m7 t2 \Jordan algebras
" q) ?9 e# o3 ^Kleene algebras" L K. ]* P/ N! M0 X0 n
Kleene lattices
% s, Z* ]( [7 n% kLambek algebras/ g; y0 R S0 a* I. i
Lattice-ordered groups
. g3 {, ?: D A/ a; ~Lattice-ordered monoids
9 u% `9 y% H& v( t' LLattice-ordered rings. p/ T5 q# B }7 C( k
Lattice-ordered semigroups: H0 U' K; ~" h6 d8 s
Lattices
0 X% H, N2 i! @; oLeft cancellative semigroups
; T5 r2 |1 G8 |5 [% \1 T; Z- dLie algebras* e% `- h c: f$ x$ C& F& T
Linear Heyting algebras
- d, u9 M0 @8 O( pLinear logic algebras
7 e( t" a3 `2 {7 yLinear orders6 w, Y/ p' I* F2 i2 u
Locales
; M8 {4 O! \0 \+ I! ^Locally compact topological spaces
8 v9 d) C# K! B! QLoops
/ p2 ]& x- |! u) F3 XLukasiewicz algebras of order n/ R% l( } A$ a' ~
M-sets
2 ]/ g' _# ]) o* TMedial groupoids$ S0 C6 V n- l: D; I
Medial quasigroups
$ I* j9 F' P2 `0 p6 IMeet-semidistributive lattices+ d7 D1 O7 ?( y; ?8 F D+ G
Meet-semilattices& P9 N/ [& \0 d6 N( Q# P
Metric spaces) m) H' |2 M& h/ e. v8 @8 F; l
Modal algebras2 X5 u0 ~( ~8 _, d3 _4 K, I
Modular lattices4 ^: W, O& s( V" P$ z+ ^3 D
Modular ortholattices
, W# V: d9 @% }Modules over a ring+ \. E% F+ s' T) H
Monadic algebras+ [" L: M3 C0 j8 f
Monoidal t-norm logic algebras
+ B$ G2 m1 Z! S: tMonoids, Finite monoids, with zero
* A! Y8 d7 t; |1 R7 @. AMoufang loops
! R3 k, Y2 M" y! O7 OMoufang quasigroups
% E% Z# l. l+ Y! nMultiplicative additive linear logic algebras/ b' ^ D, J5 O
Multiplicative lattices
/ I5 ^4 n* f) o% z, a; c, EMultiplicative semilattices) f# a4 j! ^ B: d1 w1 g1 M) }
Multisets# U9 z- ^7 i1 m& Q+ j6 Q! I" ^
MV-algebras
9 Q7 E. V- R1 G8 p- eNeardistributive lattices- R4 M r: V# O: Q; e7 |+ x! Q0 u; v
Near-rings& `" Y. L5 `; J& j- _( s; x3 O
Near-rings with identity
. }: W( b ?6 p! FNear-fields6 u8 t$ |$ y% h* n3 M
Nilpotent groups9 E# w" C" {7 f3 e) O
Nonassociative relation algebras% W! A; B+ X# G& g
Nonassociative algebras7 u; b! H! k7 T2 x7 g' g
Normal bands7 R1 z; s1 x1 D0 o5 O
Normal valued lattice-ordered groups
0 R4 N+ o+ V: }) F5 n8 QNormed vector spaces
; J/ I' R/ L7 R2 l6 i1 l& ^Ockham algebras/ s$ N* W( h0 }. q7 `
Order algebras9 T9 j8 y' j- g* c9 `; J
Ordered abelian groups2 r( D- i" W- ~) P+ ~
Ordered fields
5 Q) z {6 I* Q( q" VOrdered groups
8 u0 }+ I, U% j0 x- E( X7 AOrdered monoids# f2 K# E. r/ B4 o0 m
Ordered monoids with zero
6 m1 F. n1 m# v! FOrdered rings. y$ D5 ~0 h; Q+ Q' W% o
Ordered semigroups, Finite ordered semigroups, Finite ordered semigroups with zero7 q$ p2 I& M8 N7 z# T: k) W$ @
Ordered semilattices, Finite ordered semilattices; J0 S) e, Q8 p# n. [3 X* f$ A( }
Ordered sets. m. d4 B) L( ]8 ^
Ore domains
/ i- B! B9 r5 o! i8 u1 bOrtholattices3 X/ |+ A; S9 e& I$ [+ _
Orthomodular lattices8 K$ f1 J' d" x$ U: w p8 o) Y( g
p-groups
) N, S4 V0 \% F6 QPartial groupoids
7 W0 w' [! K7 }Partial semigroups! B+ O9 H8 O2 E) _* M
Partially ordered groups
( S0 X' G7 k" z$ s+ PPartially ordered monoids
! Y$ O/ F1 F2 J8 x' R$ J& BPartially ordered semigroups3 M, f9 z8 a+ a6 L% e( D
Partially ordered sets5 x6 |9 P4 }* G8 O2 ^/ `* x
Peirce algebras
4 e8 r; I/ T: u7 h9 M! nPocrims. N4 S8 h/ P# L
Pointed residuated lattices s3 r0 }. F4 s
Polrims
, n8 g& M4 o! a* ?Polyadic algebras8 r3 ?' K; x/ w. t' C6 I: w
Posets- U7 W/ v) A/ C! Q: N2 Y0 m2 i' _ t! O
Post algebras
1 q. }, P {, w) k: j$ _$ P( O1 ^# [Preordered sets
% b0 z1 S5 a1 p& M5 b' ~Priestley spaces" q H% J/ O% B8 |
Principal Ideal Domains' C. s9 h/ L8 E1 K0 V' w
Process algebras; x' D2 E j6 L. w1 r
Pseudo basic logic algebras
, S4 E4 Y; G" y8 g- o7 `, bPseudo MTL-algebras# |4 u8 @! z- \. S
Pseudo MV-algebras
2 @' Q3 F' ]/ S+ ]3 }! }6 |9 KPseudocomplemented distributive lattices
0 A$ j5 ?* O/ H3 t% @) `Pure discriminator algebras* M. i8 _2 |0 ]
Quantales( C- z1 `7 a% ^ ^/ S6 M
Quasigroups. c$ g; e; X9 R1 Q+ k
Quasi-implication algebras6 S" t# E+ A1 k
Quasi-MV-algebra
! j8 x& U2 ~1 _" Y/ pQuasi-ordered sets! Y7 n$ q4 a: _1 n
Quasitrivial groupoids
# h: w. o! s! k1 [Rectangular bands
- ~ z) Z5 w+ BReflexive relations6 h0 X& Y* ~$ @* z3 i1 b
Regular rings
$ N/ e# u& a$ L+ aRegular semigroups
" X) N9 M+ q! O& h0 k4 TRelation algebras
! O. E( A& s% N% L& C5 _0 }' uRelative Stone algebras) i5 n2 }- N2 r. ]1 a9 g$ _8 z
Relativized relation algebras
8 V) _% d+ D9 K) |' Q s) gRepresentable cylindric algebras/ s: Z8 Z, H4 z5 S$ e
Representable lattice-ordered groups2 {9 r1 t& a7 I( _ B7 |7 Z M6 I
Representable relation algebras
& |- g X8 g% T% iRepresentable residuated lattices
9 T p( `& J- c- `8 l* k* y- J+ B9 gResiduated idempotent semirings) b+ |7 u ]% h% c% g( Q! A
Residuated lattice-ordered semigroups8 C- m% w$ T Q. c2 b/ L$ w; [/ n
Residuated lattices
) w6 l. i) H) L0 K% ?0 xResiduated partially ordered monoids. h2 j/ p; E# J8 F7 b' h
Residuated partially ordered semigroups: r3 f- y" F& V$ u3 S
Rings
& G& Z% s+ }! l6 f6 l/ u/ M. xRings with identity
, i5 j5 k r" a" I, @+ O- e0 ySchroeder categories( B( i( n. D3 x5 S! w2 D# X2 s
Semiassociative relation algebras9 I; {4 K, Q& D/ s3 ^+ Y) M# R ?
Semidistributive lattices
9 `& k0 z p( dSemigroups, Finite semigroups
0 e" i! L9 l6 f9 b( @0 O0 C+ g: zSemigroups with identity5 ^( W8 m; J' R; u1 a0 W$ }) u9 L
Semigroups with zero, Finite semigroups with zero
" z {- j l, Z# @0 o' S, G# iSemilattices, Finite semilattices
3 M& n, _% v( Q+ ~+ F( DSemilattices with identity, Finite semilattices with identity: I. u: J1 `8 B* t
Semilattices with zero; Z. ~, I; }' s- L+ F
Semirings
# j; s6 h) }5 O% q) a3 fSemirings with identity
! B& P& g7 u/ m- c/ H: [3 [3 L( T& m9 G+ j+ tSemirings with identity and zero/ ~1 s0 i3 o* t9 B: t# g9 A- c
Semirings with zero
; I) N0 q; J1 B sSequential algebras5 b ]& C u8 m0 L; @: R9 c
Sets3 j) m% j+ D- o9 L, g
Shells) U% w3 f0 J! `4 ~3 U7 ?
Skew-fields8 `$ v; j3 T# S2 T
Skew_lattices% B: J2 `4 Z- O
Small categories
. M) l/ S1 a; w8 V \Sober T0-spaces
' n/ p( S1 D$ ]/ fSolvable groups: g* D3 ?+ D0 |( g. r, [9 {
Sqrt-quasi-MV-algebras
9 S; t# n5 X7 ]. [Stably compact spaces. r( K" W& [( `8 _
Steiner quasigroups
5 ~- a; }6 k/ N' O; I2 cStone algebras
9 r. ]- k4 X! t+ O3 `Symmetric relations9 F: N: S% V, e5 \* H
T0-spaces8 @7 E" A$ ^/ P5 w
T1-spaces, L2 l# [$ C$ n
T2-spaces4 Y. t k0 @2 V. } S7 o
Tarski algebras
* P2 ]: w. |. h' pTense algebras% F, m1 I2 u; }) E/ }1 g5 t
Temporal algebras7 Y! m7 O; t c8 X1 K
Topological groups
* m: E6 x0 u* `0 f s! K+ tTopological spaces
* Q4 y, p6 G$ |$ y" |/ YTopological vector spaces7 X/ X* f9 ~& ]2 [( T' S
Torsion groups
3 G# z2 w& o; }: y& p: ~: b- WTotally ordered abelian groups$ T1 }9 [' }- V
Totally ordered groups; i( f7 o, _' |# p# F
Totally ordered monoids2 Z+ m6 k7 Q9 v s" i& W
Transitive relations
$ c3 z2 A) y+ |4 UTrees
5 a2 z) O% a! KTournaments
0 S7 `- Q6 G( x/ j$ ^) tUnary algebras
1 L) o& L3 f. ~0 P: i1 T" GUnique factorization domains
3 w9 R: l9 t7 a2 `' y$ w& QUnital rings
J& k. W+ a% z# p3 s0 G0 X8 iVector spaces$ o& H2 T6 V' @ t# e
Wajsberg algebras
0 H1 l$ `7 e: L, UWajsberg hoops
U" e* K% U% O, V b G r) VWeakly associative lattices
: E4 o( T6 R7 Z* G" i! n* M+ H9 s' E |Weakly associative relation algebras
$ w% S# |2 o; @- j- J1 oWeakly representable relation algebras) G2 {- H1 y' o0 @% w6 Y
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