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1.
Mario Petrich 《Semigroup Forum》2005,71(3):366-388
On any regular semigroup S, the greatest idempotent pure congruence
τ the greatest idempotent separating congruence μ and the least
band congruence β are used to give the S-classification of regular semigroups as follows. These congruences generate a sublattice
Λ of the congruence lattice C(S) of S. We consider the triples (Λ,K,T), where K and T are the restrictions of the K- and T-relations
on C(S) to Λ. Such triples are characterized abstractly and form the objects of a category S whose morphisms are surjective K- and T-preserving homomorphisms subject to a mild condition. The class of regular semigroups
is made into a category S whose morphisms are fairly restricted homomorphisms. The main result of the paper is the existence of a representative functor
from S to S. The effect of the S-classification on Reilly semigroups and cryptogroups is discussed briefly. 相似文献
2.
A semigroup S is called a Clifford semigroup if it is completely regular and inverse. In this paper, some relations related to the least
Clifford semigroup congruences on completely regular semigroups are characterized. We give the relation between Y and ξ on completely regular semigroups and get that Y
* is contained in the least Clifford congruence on completely regular semigroups generally. Further, we consider the relation
Y
*, Y, ν and ε on completely simple semigroups and completely regular semigroups.
This work is supported by Leading Academic Discipline Project of Shanghai Normal University, Project Number: DZL803 and General
Scientific Research Project of Shanghai Normal University, No. SK200707. 相似文献
3.
Mario Petrich 《Semigroup Forum》2005,71(3):337-365
On any regular semigroup S, the least group congruence σ, the greatest idempotent separating congruence μ and the least band
congruence β are used to give the T-classification of regular semigroups as follows. These congruences generate a sublattice
Λ of the congruence lattice C(S) of S. We consider the triples (Λ,K,T), where K and T are the restrictions of the K- and T-relations
on C(S) to Λ. Such triples are characterized abstractly and form the objects of a category T whose morphisms are surjective K-preserving homomorphisms subject to a mild condition. The class of regular semigroups is
made into a category T whose morphisms are fairly restricted homomorphisms. The main result of the paper is the existence of a representative functor
from T to T. The effect of the T-classification to P-semigroups is considered in some detail. 相似文献
4.
具有逆断面的正则半群的同余的表示 总被引:2,自引:0,他引:2
具有道断面S°的正则半群可表示为有Saito's结构的半群W(I,S°,Λ,*,α,β).我们利用由I,S°和Λ上的同余构成的所谓同余聚抽象地表示这类半群上的同余,进而给出了这类半群的同态象的构造法. 相似文献
5.
Remmers (Adv. Math. 36:283–296, 1980) uses group diagrams in the Euclidean plane to demonstrate how equality in a semigroup S “mirrors” that inside the group G sharing the same presentation with S, when S satisfies Adyan’s condition—no cycles in the left/right graphs of the semigroup’s presentation. Goldstein and Teymouri (Semigroup
Forum 47:299–304, 1993) introduce a conjugacy equivalence relation for semigroups S. By closely examining the geometry of annular group diagrams in the plane, they show how their equivalence relation mirrors
conjugacy inside G, for S satisfying Adyan’s. In this article we introduce two cancellative commutative congruences. Following their leads, we examine
the geometry of group diagrams on closed surfaces of higher genera to demonstrate how these congruences mirror equality inside
two naturally associated Abelian quotient groups G/[G,G] and G/G
2, respectively. In these instances we can drop Adyan’s condition. 相似文献
6.
Petrich 《Semigroup Forum》2008,66(2):179-211
Abstract. On any regular semigroup S, the least group congruence σ, the greatest idempotent pure congruence τ and the least band congruence β are used to give the M -classification of regular semigroups as follows. These congruences generate a sublattice Λ of the congruence lattice C
(S) of S. We consider the triples (Λ,K,T), where K and T are the restrictions of the K - and T -relations on {C
(S) to Λ. Such triples are characterized abstractly and form the objects of a category M whose morphisms are surjective T -preserving homomorphisms subject to a mild condition. The class of regular semigroups is made into a category M whose morphisms are fairly restricted homomorphisms. The main result of the paper is the existence of a representative functor
from M to M. Several properties of the classification of regular semigroups induced by this functor are established. 相似文献
7.
Let S° be an inverse semigroup with semilattice biordered set E° of idempotents and E a weakly inverse biordered set with a subsemilattice Ep = { e ∈ E | arbieary f ∈ E, S(f , e) loheain in w(e)} isomorphic to E° by θ:Ep→E°. In this paper, it is proved that if arbieary f, g ∈E, f ←→ g→→ f°θD^s° g°θand there exists a mapping φ from Ep into the symmetric weakly inverse semigroup P J(E∪ S°) satisfying six appropriate conditions, then a weakly inverse semigroup ∑ can be constructed in P J(S°), called the weakly inverse hull of a weakly inverse system (S°, E, θ, φ) with I(∑) ≌ S°, E(∑) ∽- E. Conversely, every weakly inverse semigroup can be constructed in this way. Furthermore, a sufficient and necessary condition for two weakly inverse hulls to be isomorphic is also given. 相似文献
8.
Shichao Chen 《The Ramanujan Journal》2009,18(1):103-112
Let Λ={λ
1≥⋅⋅⋅≥λ
s
≥1} be a partition of an integer n. Then the Ferrers-Young diagram of Λ is an array of nodes with λ
i
nodes in the ith row. Let λ
j
′ denote the number of nodes in column j in the Ferrers-Young diagram of Λ. The hook number of the (i,j) node in the Ferrers-Young diagram of Λ is denoted by H(i,j):=λ
i
+λ
j
′−i−j+1. A partition of n is called a t-core partition of n if none of the hook numbers is a multiple of t. The number of t-core partitions of n is denoted by a(t;n). In the present paper, some congruences and distribution properties of the number of 2
t
-core partitions of n are obtained. A simple convolution identity for t-cores is also given.
相似文献
9.
Attila Nagy 《Semigroup Forum》2008,76(2):297-308
We say that a semigroup S is a permutable semigroup if the congruences of S commute with each other, that is, α○β=β○α is satisfied for all congruences α and β of S. A semigroup is called a medial semigroup if it satisfies the identity axyb=ayxb. The medial permutable semigroups were examined in Proc. Coll. Math. Soc. János Bolyai, vol. 39, pp. 21–39 (1981), where the medial semigroups of the first, the second and the third kind were characterized, respectively. In Atta Accad.
Sci. Torino, I-Cl. Sci. Fis. Mat. Nat. 117, 355–368 (1983) a construction was given for medial permutable semigroups of the second [the third] kind. In the present paper we give a
construction for medial permutable semigroups of the first kind. We prove that they can be obtained from non-archimedean commutative
permutable semigroups (which were characterized in Semigroup Forum 10, 55–66, 1975).
Research supported by the Hungarian NFSR grant No T042481 and No T043034. 相似文献
10.
Recall that the semigroups S and R are said to be strongly Morita equivalent if there exists a unitary Morita context (S, R.,
S
P
R,R
Q
S
,〈〉
, ⌈⌉) with 〈〉 and ⌈⌉ surjective. For a factorisable semigroup S, we denote ζ
S
= {(s
1, s
2) ∈S×S|ss
1 = ss
2, ∀s∈S}, S' = S/ζ
S
and US-FAct = {
S
M∈S− Act |SM = M and SHom
S
(S, M) ≅M}. We show that, for factorisable semigroups S and M, the categories US-FAct and UR-FAct are equivalent if and only if the semigroups S' and R' are strongly Morita equivalent. Some conditions for a factorisable semigroups to be strongly Morita equivalent to a sandwich
semigroup, local units semigroup, monoid and group separately are also given. Moreover, we show that a semigroup S is completely simple if and only if S is strongly Morita equivalent to a group and for any index set I, S⊗SHom
S
(S, ∐
i∈I
S) →∐
i∈I
S, s⊗t·ƒ↦ (st)ƒ is an S-isomorphism.
The research is partially supported by a UGC(HK) grant #2160092.
Project is supported by the National Natural Science Foundation of China 相似文献
11.
According to A. Beurling and H. Landau, if an exponential system {e
iλt
}λ∈Λ is a frame in L
2 on a set S of positive measure, then Λ must satisfy a strong density condition. We replace the frame concept by a weaker condition and
prove that if S is a finite union of segments then the result holds. However, for “generic” S, very sparse sequences Λ are admitted.
Supported in part by the Israel Science Foundation. 相似文献
12.
Let I be an interval of positive rational numbers. Then the set S (I) = T ∩ N, where T is the submonoid of (Q0+, +) generated by T, is a numerical semigroup. These numerical semigroups are called proportionally modular and can be characterized as the set of integer solutions of a Diophantine inequality of the form ax rood b 〈 cx. In this paper we are interested in the study of the maximal intervals I subject to the condition that S (I) has a given multiplicity. We also characterize the numerical semigroups associated with these maximal intervals. 相似文献
13.
Mario Petrich 《Semigroup Forum》2011,83(3):412-446
Let S be a semigroup and s,t∈S. We say that t is an associate of s if s=sts. If S has a maximal subgroup G such that every element s of S has a unique associate in G, say s
∗, we say that G is an associate subgroup of S and consider the mapping s→s
∗ as a unary operation on S. In this way, semigroups with an associate subgroup may be identified with unary semigroups satisfying three simple axioms.
Among them, only those satisfying the identity (st)∗=t
∗
s
∗, called medial, have a structure theorem, due to Blyth and Martins. 相似文献
14.
Xilin Tang 《代数通讯》2013,41(11):5439-5461
15.
本文研究了N(2,2,0)代数(S,*,△,0)的E-反演半群.利用N(2,2,0)代数的幂等元,弱逆元,中间单位元的性质和同宇关系,得到了N(2,2,0)代数的半群(S,*)构成E-反演半群的条件及元素α的右伴随非零零因子唯一,且为α的弱逆元等结论,这些结果进一步刻画了N(2,2,0)代数的结构. 相似文献
16.
Primož Moravec 《Semigroup Forum》2008,77(2):316-324
In this paper we find simple characterizations of completely simple semigroups with H-classes nilpotent of class ≤c, and of completely simple semigroups whose core has H-classes nilpotent of class ≤c. The notion of w-marginal completely regular semigroups is introduced, generalizing the concept of central semigroups. A law characterizing
[x
1,x
2,…,x
c+1]-marginal completely simple semigroups is obtained. Additionally, the least congruences corresponding to these classes are
described. Our results extend the corresponding results obtained by Petrich and Reilly in the abelian case.
The author was supported by the Ministry of Higher Education, Science and Technology of Slovenia. 相似文献
17.
18.
We give ?-congruences on an abundant semigroup with an SQ-adequate transversal S ° by the ?-congruence triple abstractly which consists of congruences on the structure component parts L, T and R. We prove that the set of all ?-congruences on this kind of semigroups is a complete lattice. 相似文献
19.
Sefi Ladkani 《Algebras and Representation Theory》2011,14(1):57-74
A triangular matrix ring Λ is defined by a triplet (R,S,M) where R and S are rings and
R
M
S
is an S-R-bimodule. In the main theorem of this paper we show that if T
S
is a tilting S-module, then under certain homological conditions on the S-module M
S
, one can extend T
S
to a tilting complex over Λ inducing a derived equivalence between Λ and another triangular matrix ring specified by (S′, R, M′), where the ring S′ and the R-S′-bimodule M′ depend only on M and T
S
, and S′ is derived equivalent to S. Note that no conditions on the ring R are needed. These conditions are satisfied when S is an Artin algebra of finite global dimension and M
S
is finitely generated. In this case, (S′,R,M′) = (S, R, DM) where D is the duality on the category of finitely generated S-modules. They are also satisfied when S is arbitrary, M
S
has a finite projective resolution and Ext
S
n
(M
S
, S) = 0 for all n > 0. In this case, (S′,R,M′) = (S, R, Hom
S
(M, S)). 相似文献
20.
It is proved that all the equivalence relations of a universal algebra A are its congruences if and only if either |A| ≤ 2 or every operation f of the signature is a constant (i.e., f(a
1
, . . . , a
n
) = c for some c ∈ A and all the a
1
, . . . , a
n
∈ A) or a projection (i.e., f(a
1
, . . . , a
n
) = a
i
for some i and all the a
1
, . . . , a
n
∈ A). All the equivalence relations of a groupoid G are its right congruences if and only if either |G| ≤ 2 or every element a ∈ G is a right unit or a generalized right zero (i.e., x
a
= y
a
for all x, y ∈ G). All the equivalence relations of a semigroup S are right congruences if and only if either |S| ≤ 2 or S can be represented as S = A∪B, where A is an inflation of a right zero semigroup, and B is the empty set or a left zero semigroup, and ab = a, ba = a
2 for a ∈ A, b ∈ B. If G is a groupoid of 4 or more elements and all the equivalence relations of it are right or left congruences, then either all
the equivalence relations of the groupoid G are left congruences, or all of them are right congruences. A similar assertion for semigroups is valid without the restriction
on the number of elements. 相似文献