Homogeneity of the radical of semigroup-graded rings

We show that cancellativity is a necessary condition on a semigroup S for the Jacobson radical of all S-graded rings to be homogeneous. We introduce some related classes of semigroups S for which the Jacobson radical of certain S-graded rings is always homogeneous. Commutative and regular semigroups in these classes are described     

Basic properties of e-inversive semigroups

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.     

Seminearrings,seminearfields and their semigroup-theoretical background

In this paper we deal with some basic properties of seminearrings (S,+,·), in particular with respect to multiplicative cancellativity (§2) and to seminearfields (§3, §4). All seminearrings of order 2 are listed in §5. In general, we do not assume that (S,+) is associative. Moreover, we present most of our results as consequences of corresponding statements on semigroups (S,·). Clearly, all results apply to semirings and nearrings, particularly to those with associative addition, and some of them will be new also in this context. Dedicated to Professor L. M. Gluskin on his 60th birthday     

正规Ehresmann型wrpp半群

众所周知,Clifford半群是正则半群类中的一类重要半群,本文定义正规 Ehresmann型wrpp半群,它是Clifford半群在wrpp半群类中的推广,给出了此类半群的若干刻划.     

On C*-quasiregular semigroups *

In this paper, we introduce an important subclass of quasiregular semigroups, namely the class of C^*-quasiregular semigroups. This class of semigroups contains the classes of Clifford semigroups, quasi Clifford semigroups, C-quasiregular semigroups and their generalizations as its subclasses. Some characterization theorems for such semigroups are obtained. The structure of this kind of quasiregular semigroups is investigated by using the generalized ?-product of some semigroups on a semilattice Y. Construction techniques of such classes of semigroups are particularly demonstrated.     

Super rpp semigroups

We study a class of special strongly rpp semigroups, namely, the class of super rpp semigroups. These super rpp semigroups are generalizations of both superabundant semigroups and Clifford semigroups within the class of rpp semigroups. In particular, we prove that a super rpp semigroup is a semilattice of D ^(l)-simple strongly rpp semigroups. Our result not only generalizes a well-known theorem of Clifford in the class of completely regular semigroups but also strengthens some structure theorems obtained by Ren-Shum for superabundant semigroups which are orthodox. Some special super rpp semigroups are considered and discussed.     

关于强可逆半准素序半群

把由G．Thierrin和A．Spoletini-Cherubini等人定义并研究的强可逆半群以及由S．Bogdanovic研究的半准素半群分别推广为强可逆序半群和半准素序半群．分别给出了半准素序半群和强可逆序半群类中的半准素序半群的刻划，还给出了其所有理想是素理想的强可逆序半群的刻划．     

Semigroups of mappings on graphs

At present, there are quite a few investigations in the theory of semigroups devoted to semigroups of mappings on graphs. Up to now, endomorphism semigroups of graphs, extensive transformation semigroups of graphs, coloring semigroups of graphs and other semigroups of special mappings on graphs have been studied. The results obtained show the way graphs are determined by the above-mentioned semigroups. They also show the structure of semigroups of mappings and interrelations between properties of graphs and corresponding properties of semigroups associated with the graphs. This paper gives a survey of the main results in this field.     

纯整Ehresmann半群的若干刻划

本文介绍纯整Ehresmann半群．纯整Ehresmann半群是一类特殊的U-半富足半群，我们给出了这类半群的若干刻划，并讨论了一些特殊的纯整Ehresmann半群．     

Context equivalence of semigroups

Two semigroups are called strongly Morita equivalent if they are contained in a Morita context with unitary bi-acts and surjective mappings. We consider the notion of context equivalence which is obtained from the notion of strong Morita equivalence by dropping the requirement of unitariness. We show that context equivalence is an equivalence relation on the class of factorisable semigroups and describe factorisable semigroups that are context equivalent to monoids or groups, and semigroups with weak local units that are context equivalent to inverse semigroups, orthodox semigroups or semilattices.     

On Locally Inverse Semigroups Having Weakly E-unitary Covers

Recently, Billhardt has characterized the locally inverse semigroups embeddable in Rees matrix semigroups over generalized inverse semigroups. We prove here that these semigroups are just the locally inverse semigroups having weakly E-unitary covers.     

Semigroups with the ideal retraction property

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.     

Semigroups with the ideal retraction property

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.     

Free orthodox semigroups and free bands with inverse transversals

It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular semigroups with inverse transversals does not belong to this variety. We now call this class of semigroups the ist-variety of semigroups, and denote it by IST. In this paper, we consider the class of orthodox semigroups with inverse transversals, which is a special ist-variety and is denoted by OIST. Some previous results given by Tang and Wang on this topic are extended. In particular, the structure of free bands with inverse transversals is investigated. Results of McAlister, McFadden, Blyth and Saito on semigroups with inverse transversals are hence generalized and enriched.     

Weakly Strict Regular Semigroups

Weakly strict regular semigroups WS represent a generalization of strict regular semigroups. For the intersection of WS with some usual e-varieties of regular semigroups, such as left regular orthodox semigroups and similar e-varieties V, we provide WS ⋂ V with a basis of identities and forbidden semigroups. The latter, by exclusion, characterize the given e-variety. We do this also for WS. Coupled with some results of Hall, Churchill and Trotter, we characterize in this way also the e-varieties of completely regular semigroups as well as regular semigroups which are locally completely regular. The e-varieties studied are depicted in a diagram.     

On Weierstrass semigroups of double covering of genus two curves

In this work we prove that are Weierstrass semigroups all numerical semigroups whose three first positive non-gaps are 6, 8 and 10, resolving the problem of the numerical semigroups that appear as Weierstrass semigroups in double coverings of genus two curves.     

扰动双参数C_0半群的直接范数连续性

双参数半群理论是研究Markov过程的一种重要方法.本文首先证明了双参数C_0半群在有界扰动下生成一个双参数C_0半群;其次证明了如果双参数C_0半群是直接范数连续的,那么在有界扰动下生成的双参数C_0半群也是直接范数连续的.     

Quasi-C-Ehresmann Semigroups and Their Subclasses

We introduce the concept of a quasi-C-Ehresmann semigroup. Some special quasi-C-Ehresmann semigroups will be considered. We will show that the quasi-C-Ehresmann semigroups are special U-semiabundant semigroups and orthodox U-liberal semigroups, which have been recently studied by several authors. Some characterization theorems of this new class of semigroups are obtained. Many results of quasi-C-semigroups in the literature can be extended to quasi-C-Ehresmann Semigroups.     

直觉模糊变换半群的积与覆盖关系

提出了直觉模糊变换半群的(全)直积,圈积,直觉模糊变换半群的覆盖的定义,利用代数的手段讨论了直觉模糊变换半群的积的结合性质,研究了直觉模糊变换半群的积的覆盖关系.     

Ordered semigroups whose elements are separated by prime ideals

In this paper we add one more characterization of intra-regular ordered semigroups in the existing bibliography by proving that the ordered semigroups whose elements are separated by prime ideals are actually the intra-regular ordered semigroups, a result which generalizes the corresponding result of semigroups (without order).