共查询到20条相似文献,搜索用时 15 毫秒
1.
The construction by Hall of a fundamental orthodox semigroup W
B
from a band B provides an important tool in the study of orthodox semigroups. We present here a semigroup S
B
that plays the role of W
B
for a class of semigroups having a band of idempotents B. Specifically, the semigroups we consider are weakly B-abundant and satisfy the congruence condition (C). Any orthodox semigroup S with E(S)=B lies in our class. On the other hand, if a semigroup S lies in our class, then S is Ehresmann if and only if B is a semilattice.
The Hall semigroup W
B
is a subsemigroup of S
B
, as are the (weakly) idempotent connected semigroups V
B
and U
B
. We show how the structure of S
B
can be used to extract information relating to arbitrary weakly B-abundant semigroups with (C).
This work was carried out during a visit to Lisbon of the second author funded by the London Mathematical Society and while
the first author was a member of project POCTI/0143/2003 of CAUL financed by FCT and FEDER. 相似文献
2.
If S is a semigroup, the global (or the power semigroup) of S is the set P(S) of all nonempty subsets of S equipped with a naturally defined multiplication. A class K of semigroups is globally determined if any two semigroups of K with isomorphic globals are themselves isomorphic. We study properties of globals of idempotent semigroups and show, in particular, that the class of normal bands is globally determined. 相似文献
3.
本文首先研究了具有可消模断面的拟恰当半群的结构,然后给出了用可消模断面的拟恰当半群构造具有CO-恰当断面富足半群的方法. 相似文献
4.
《代数通讯》2013,41(8):2929-2948
Abstract A semigroup S is called E-inversive if for every a ∈ S there is an x ∈ S such that ax is idempotent. The purpose of this paper is the investigation of E-inversive semigroups and semigroups whose idempotents form a subsemigroup. Basic properties are analysed and, in particular, semigroups whose idempotents form a semilattice or a rectangular band are considered. To provide examples and characterizations, the construction methods of generalized Rees matrix semigroups and semidirect products are employed. 相似文献
5.
6.
In this paper we establish a construction of a class of left E-adequate semigroups by using semilattices of cancellative monoids and fundamental left E-adequate semigroups. We first introduce concepts of type μ^+(μ^*,μ ) abundant semigroups and type μ^+left E-adequate semigroups. In fact, regular semigroups are type μ^+abundant semigroups and inverse semigroups are type μ^+left E-adequate semigroups. Next, we construct a special kind of algebras called E^+-product. It is proved that every E^+-product is a type μ^+left E-adequate semigroup, and every type μ^+left E-adequate semigroup is isomorphic to an E^+-product of a semilattice of cancellative monoids with a fundamental left E-adequate semigroup. Finally, as a corollary of the main result, it is deduced that every inverse semigroup is isomorphic to an E^+-product of a Clifford semigroup by a fundamental inverse semigroup. 相似文献
7.
8.
In this article we prove that if S is a faithfully projective R-algebra and H is a finite inverse semigroup acting on S as R-linear maps such that the fixed subring S H = R, then any partial isomorphism between ideals of S which are generated by central idempotents can be obtained as restriction of an R-automorphism of S and there exists a finite subgroup of automorphisms G of S with S G = R. 相似文献
9.
10.
E. V. Shulman 《Functional Analysis and Its Applications》2005,39(4):314-316
Let a representation T of a semigroup G on a linear space X be given. We call x ∈ X a finite vector if its orbit T(G) is contained in a finite-dimensional subspace. In this paper, some statements about finite vectors are applied to the following problem. For a given positive integer n > 1, describe all continuous functions f : G → ? such that the function (x1,..., x n ) ? f(x1 + ? + x n ) can be polynomially expressed via functions of sums of fewer variables. 相似文献
11.
Bernd Billhardt 《代数通讯》2013,41(10):3629-3641
A regular semigroup S is termed locally F-regular, if each class of the least completely simple congruence ξ contains a greatest element with respect to the natural partial order. It is shown that each locally F-regular semigroup S admits an embedding into a semidirect product of a band by S/ξ. Further, if ξ satisfies the additional property that for each s ∈ S and each inverse (sξ)′ of sξ in S/ξ the set (sξ)′ ∩ V(s) is not empty, we represent S both as a Rees matrix semigroup over an F-regular semigroup as well as a certain subsemigroup of a restricted semidirect product of a band by S/ξ. 相似文献
12.
A finite semigroup S is said to preserve finite generation (resp., presentability) in direct products, provided that, for every infinite semigroup T, the direct product S × T is finitely generated (resp., finitely presented) if and only if T is finitely generated (resp., finitely presented). The main result of this paper is a constructive necessary and sufficient condition for S to preserve both finite generation and presentability in direct products. The condition is that certain graphs, (s), one for each s S, are all connected. The main result is illustrated in three examples, one of which exhibits a 4-element semigroup that preserves finite generation but not finite presentability in direct products.1991 Mathematics Subject Classification: 20M05, 05C25The first author is financially supported by the Sub-Programa Ciência e Tecnologia do 2° Quadro Comunitário de Apoio (grant number BD/ 15623/98). The author also acknowledges the support of the Centro de Álgebra da Universidade de Lisboa and of the Projecto Praxis 2/2.1/MAT/73/94. The second author acknowledges partial financial support from the Nuffield Foundation. 相似文献
13.
Recep Korkmaz 《Semigroup Forum》2009,78(3):528-535
In this paper we study dense inverse subsemigroups of topological inverse semigroups. We construct a topological inverse semigroup
from a semilattice. Finally, we give two examples of the closure of B
( −∞, ∞ )1, a topological inverse semigroup obtained by starting with the real numbers as a semilattice with the operation a
∨
b=sup{a,b}.
The author would like to thank to the referee for useful suggestions. 相似文献
14.
Kunitaka Shoji 《代数通讯》2013,41(8):3278-3289
In this article, we prove that the full transformation semigroup on a finite set is an amalgamation base for finite semigroups. 相似文献
15.
16.
It is known that the semigroup Sing n of all singular self-maps of X n = {1,2,…, n} has rank n(n ? 1)/2. The idempotent rank, defined as the smallest number of idempotents generating Sing n , has the same value as the rank. (See Gomes and Howie, 1987.) Idempotents generating Sing n can be seen as special cases (with m = r = 2) of (m, r)-path-cycles, as defined in Ay\i k et al. (2005). The object of this article is to show that, for fixed m and r, the (m, r)-rank of Sing n , defined as the smallest number of (m, r)-path-cycles generating Sing n , is once again n(n ? 1)/2. 相似文献
17.
本文主要研究了具有乘适当断面无交并性质的富足半群的若干性质,并证明了半群为具有乘适当断面无交并性质的富足半群当且仅当它是一个矩形带和适当半群的直积。 相似文献
18.
《代数通讯》2013,41(5):1917-1935
Abstract For a set X, an equivalence relation ρ on X, and a cross-section R of the partition X/ρ induced by ρ, consider the semigroup T(X, ρ, R) consisting of all mappings a from X to X such that a preserves both ρ (if (x, y)?∈?ρ then (xa, ya)?∈?ρ) and R (if r?∈?R then ra?∈?R). The semigroup T(X, ρ, R) is the centralizer of the idempotent transformation with kernel ρ and image R. We determine the structure of T(X, ρ, R) in terms of Green's relations, describe the regular elements of T(X, ρ, R), and determine the following classes of the semigroups T(X, ρ, R): regular, abundant, inverse, and completely regular. 相似文献
19.
Let S =∪(Gα : α ∈ E) be a semilattice of groups(i.e., a Cliford semigroup) and n a natural number. E is called an n-element chain of groups if it is an n-element chain. Denote by Cn the set of all n-element chains of groups. In this paper we shall show that for any natural number n, the class of semigroups Cn satisfies the strong isomorphism property. 相似文献
20.