共查询到20条相似文献,搜索用时 31 毫秒
1.
Xiaojiang Guo 《Semigroup Forum》2003,66(3):368-380
The aim of this paper is to study and characterize compact semigroups with the ideal extension property. We establish a characterization of compact semigroups having the ideal extension property. In particular, we completely determine the structure of such semigroups with the property that regular elements form a subsemigroup, and also the structure of such semigroups with precisely one regular D-class. 相似文献
2.
The congruence extension property (CEP) of semigroups has been extensively studied by a number of authors. We call a compact semigroup S an Ω-compact semigroup if the set of all regular elements of S forms an ideal of S. In this note, we characterize the Ω-compact semigroup having (CEP). Our result extends a recent result obtained by X.J. Guo on the congruence extension property of strong Ω-compact semigroups which is a semigroup containing precisely one regular D-class. 相似文献
3.
Xiaojiang Guo 《Semigroup Forum》2004,69(1):102-112
The aim of this paper is to study the congruence
extension property and the ideal extension property
for compact semigroups. We present a characterization of compact
semigroups with the ideal extension property and prove that each compact semigroup
with the congruence extension property also has the ideal extension property. 相似文献
4.
Abstract. In this paper we investigate the structure of semigroups with the ideal retraction property i.e., semigroups which are not
simple and have the property that each ideal is a homomorphic retract of the semigroup.
We present examples to show that the ideal retraction property is neither hereditary nor productive. That this property is
preserved by homomorphisms is established for some classes of semigroups, but the general question remains open.
The classes of semigroups investigated in this paper are separative semigroups, ideal semigroups, semilattices, cyclic semigroups,
nil semigroups, and Clifford semigroups.
It is established that a semigroup with zero 0 which is expressible as a direct sum of each ideal and a dual ideal (complement
with 0 adjoined) has the ideal retraction property. The converse holds for ideal semigroups, and an example is presented which
demonstrates that the converse does not hold in general. 相似文献
5.
N. Kehayopulu 《Russian Mathematics (Iz VUZ)》2009,53(2):41-58
Following the well-known Schreier extension of groups, the (ideal) extension of semigroups (without order) have been first
considered by A. H. Clifford in Trans. Amer. Math. Soc. 68 (1950), with a detailed exposition of the theory in the monographs of Clifford-Preston and Petrich. The main theorem of the
ideal extensions of ordered semigroups has been considered by Kehayopulu and Tsingelis in Comm. Algebra 31 (2003). It is natural to examine the same problem for lattices. Following the ideal extensions of ordered semigroups, in
this paper we give the main theorem of the ideal extensions of lattices. Exactly as in the case of semigroups (ordered semigroups),
we approach the problem using translations. We start with a lattice L and a lattice K having a least element, and construct (all) the lattices V which have an ideal L′ which is isomorphic to L and the Rees quotient V|L′ is isomorphic to K. Conversely, we prove that each lattice which is an extension of L by K can be so constructed. An illustrative example is given at the end.
The text was submitted by the author in English. 相似文献
6.
Jean-Camille Birget 《Journal of Pure and Applied Algebra》1984,34(1):57-115
The notion of regularity for semigroups is studied, and it is shown that an unambiguous semigroup (i.e., whose and orders are respectively unions of disjoint trees) can be embedded in a regular semigroup with the same subgroups and the same ideal structure (except that a zero is added to the regular semigroup).In a previous paper [1] it was shown that any semigroup is the homomorphic image of an unambiguous semigroup with the same groups and a similar ideal structure.Together these two papers thus prove that an arbitrary semigroup divides a regular semigroup with a similar structure.The resulting regular semigroup is finite (resp. torsion, or bounded torsion) if the given semigroup has that property. 相似文献
7.
《代数通讯》2013,41(6):2061-2085
Abstract The aim of this paper is to study some special lpp-semigroups, namely, the left GC-lpp semigroups. After obtaining some properties and characterizations of such semigroups, we establish some structure theorems of this class of semigroups. In addition, we also consider some special cases. As an application, we describe the structure theorems of IC quasi-adequate semigroups whose idempotent band is a regular band. 相似文献
8.
A. Van Daele 《代数通讯》2013,41(6):2341-2386
A simple and nice structure theorem for orthogroups was given by Petrich in 1987. In this paper, we consider a generalized orthogroup, that is, a quasi-completely regular semigroup with a band of idempotents in which its set of regular elements, namely, RegS, forms an ideal of S. A method of construction of such semigroups is provided and as a result, the Petrich structure theorem of orthogroups becomes an immediate corollary of our theorem on generalized orthogroups. An example of such generalized orthogroup is also constructed. This example provides some useful information for the construction of various kinds of quasi-completely regular semigroups. 相似文献
9.
Dr. A. Mukherjea 《Probability Theory and Related Fields》1969,11(2):142-146
Summary In this paper, idempotent probability measures have been considered on semigroups which are locally compact or metric and satisfy: (*) A
–1
B and Ax
–1 are compact whenever A and B are so, for every x in the semigroup. Such semigroups are more general than compact semigroups which do admit of such measures. On such semigroups we can construct such measures by the usual process if there is a compact sub-semigroup. It is shown in this paper that if such a measure exists in such semigroups, then it must be such an extension measure. Some related results concerning the conditions (*) are also discussed here. 相似文献
10.
The p
n
-sequence of a semigroup S is said to be polynomially bounded, if there exist a positive constant c and a positive integer r such that the inequality p
n
(S) ≤cn
r
holds for all n≥ 1. In this paper, we fully describe all finite semigroups having polynomially bounded p
n
-sequences. First we give a characterization in terms of identities satisfied by these semigroups. In the sequel, this result
will allow an insight into the structure of such semigroups. We are going to deal with certain ideals and the construction
of ideal extension of semigroups. In addition, we supply an effective procedure for deciding whether a finite semigroup has
polynomially bounded p
n
-sequence and give some examples.
Received March 5, 1999; accepted in final form November 1, 1999. 相似文献
11.
ABSTRACT The investigation of regular F-abundant semigroups is initiated. In fact, F-abundant semigroups are generalizations of regular cryptogroups in the class of abundant semigroups. After obtaining some properties of such semigroups, the construction theorem of the class of regular F-abundant semigroups is obtained. In addition, we also prove that a regular F-abundant semigroup is embeddable into a semidirect product of a regular band by a cancellative monoid. Our result is an analogue of that of Gomes and Gould on weakly ample semigroups, and also extends an earlier result of O'Carroll on F-inverse semigroups. 相似文献
12.
Generalizing a property of regular resp. finite semigroups a semigroup S is called E-(0-) inversive if for every a ∈ S4(a ≠ 0) there exists x ∈ S such that ax (≠ 0) is an idempotent. Several characterizations are given allowing to identify the (completely, resp. eventually) regular semigroups in this class. The case that for every a ∈ S4(≠ 0) there exist x,y ∈ S such that ax = ya(≠ 0) is an idempotent, is dealt with also. Ideal extensions of E- (0-)inversive semigroups are studied discribing in particular retract extensions of completely simple semigroups. The structure of E- (0-)inversive semigroups satisfying different cancellativity conditions is elucidated. 1991 AMS classification number: 20M10. 相似文献
13.
《代数通讯》2013,41(7):2609-2615
Abstract Regular semigroups S with the property eS ? Se or Se ? eS for all idempotents e ∈ S include all left and right Clifford semigroups. Characterizations of such semigroups are given and their structure investigated, in particular in terms of spined products of left and right Clifford semigroups with respect to Clifford semigroups. 相似文献
14.
K.D. Aucoin 《Semigroup Forum》1999,58(2):175-189
In this paper, we will characterize commutative semigroups which have the ideal extension property (IEP). This characterization describes the multiplicative structure of commutative semigroups with IEP. Establishing this characterization was motivated not only by an interest in IEP itself, but also by the fact that in the category of commutative semigroups, the congruence extension property (CEP) implies IEP. A few preliminary results which hold in the general (non-commutative) case are discussed below. Following these initial observations, all semigroups considered are commutative. 相似文献
15.
Jorge Martínez 《Algebra Universalis》2006,55(1):13-43
One considers the poset of dense, coherent frame quotients of an algebraic frame with the finite intersection property, which
are compact. It is shown that there is a smallest such, the frame of d-elements. However, unless the frame is already compact there is no largest such quotient.
With the additional assumption of disjointification on the frame, one then studies the maximal ideal spaces of these quotients
and the relationship to covers of compact spaces.
Several applications are considered, with considerable attention to the frame quotients defined by extension of ideals of
a commutative ring A to a ring extension; this type of frame quotient is considered both with and without an underlying lattice structure on the
rings.
Received January 8, 2005; accepted in final form August 28, 2005. 相似文献
16.
We consider the question of membership of A ∨ G, where A and G are the pseudovarieties of finite aperiodic semigroups, and finite groups, respectively. We find a straightforward criterion
for a semigroup S lying in a class of finite semigroups that are weakly abundant, to be in A ∨ G. The class of weakly abundant semigroups contains the class of regular semigroups, but is much more extensive; we remark
that any finite monoid with semilattice of idempotents is weakly abundant. To study such semigroups we develop a number of
techniques that may be of interest in their own right. 相似文献
17.
Karen D. Aucoin 《Semigroup Forum》1996,52(1):157-162
A topological semigroupS is said to have thecongruence extension property (CEP) provided that for each closed subsemigroupT ofS and each closed congruence σ onT, σ can be extended to a closed congruence
onS. (That is,
∩(T xT=σ). The main result of this paper gives a characteriation of Γ-compact commutative archimedean semigroups with the congruence
extension property (CEP). Consideration of this result was motivated by the problem of characterizing compact commutative
semigroups with CEP as follows. It is well known that every commutative semigroup can be expressed as a semilattice of archimedean
components each of which contains at most one idempotemt. The components of a compact commutative semigroup need not be compact
(nor Γ-compact) as the congruence providing the decomposition is not necessarily closed. However, any component with CEP which
is Γ-compact is characterized by the afore-mentioned result. Characterization of components of a compact commutative semigroup
having CEP is a natural step towar characterization of the entire semigroup since CEP is a hereditary property. Other results
prevented in this paper give a characterization of compact monothetic semigroups with CEP and show that Rees quotients of
compact semigroups with CEP retain CEP. 相似文献
18.
Abstract. A topologized semigroup is called perfect if its multiplication is a perfect map (= a closed continuous mapping such that the inverse image of every point is compact).
Thus a locally compact topological semigroup is perfect if and only if its multiplication is closed and each of its elements
is compactly divided , that is, its divisors form a compact set. In the present paper we study compactly and non-compactly divided elements in
the contexts of general locally compact semigroups, subsemigroups of groups, Lie semigroups and subsemigroups of Sl(2,R). 相似文献
19.
《代数通讯》2013,41(11):4465-4484
Abstract We generalise theory of Lawson for inverse monoids with zero to wider classes of regular semigroups. We give a structure theorem for ?-unipotent monoids with zero. Several connections between cancellative categories and 0-E-unitary semigroups are obtained as an application of the results of this paper. 相似文献