带恰当断面的拟-型$\delta$半群

In this paper,some properties of quasi-type δ semigroups with an adequate transversal are explored.In particular,abundant semigroups with a cancellative transversal are character-ized.Our results generalize and enrich Saito＇s results on quasi-orthodox semigroups with an inverse transversal.     

带有乘右适当断面的右主投射半群(英文)

In this paper,the concept of right adequate transversals of rpp semigroups is introduced.We establish the structure of rpp semigroups with multiplicative right adequate transversals in terms of right normal bands and right adequate semigroups.In particular, some special cases are considered.     

On generalized inverse transversals

Let S be a regular semigroup, S° an inverse subsemigroup of S.S° is called a generalized inverse transversal of S, if V（x）∩S°≠Ф. In this paper, some properties of this kind of semigroups are discussed. In particular, a construction theorem is obtained which contains some recent results in the literature as its special cases.     

左C-wrpp 半群的左$\Delta$-积

We study another structure of so-called left C-wrpp semigroups. In particular, the concept of left △-product is extended and enriched. The aim of this paper is to give a construction of left C-wrpp semigroups by a left regular band and a strong semilattice of left-R cancellative monoids. Properties of left C-wrpp semigroups endowed with left △-products are particularly investigated.     

关于具有$Q$-逆断面的正则半群的同余格

In this paper, a complete congruence on the congruence lattice of regular semigroups with Q-inverse transversals is analysed. The classes of this complete congruence which are intervals are discussed and their least and greatest elements are presented clearly.     

A Class of Left E-adequate Semigroups

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.     

GV-半群的若干刻画

GV-semigroups are the generalizations of completely regular semigroups in the range ofπ-regular semigroups.In this paper,Green~*-relations on GV-semigroups and some congruences on it are studied.     

Trotter—Kato Theorems for an α—times Integrated Semigroups

In this paper,we discuss on the convergence and approximation of an α-times integrated semigroups. The Trotter-kato theorems for an α-times integrated semigroups are obtained.     

可分裂的左GC-lpp半群

A left GC-lpp semigroup S is called split if the natural homomorphism γb of S onto S/γ induced by γ is split.It is proved that a left GC-lpp semigroup is split if and only if it has a left adequate transversal.In particular,a construction theorem for split left GC-lpp semigroups is established.     

Split Left GC-Lpp Semigroups

A left GC-lpp semigroup S is called split if the natural homomorphism γb of S onto S/γ induced by γ is split.It is proved that a left GC-lpp semigroup is split if and only if it has a left adequate transversal.In particular,a construction theorem for split left GC-lpp semigroups is established.     

SOME REMARKS ON （L）-GREEN’S RELATIONS AND STRONGLY RPP SEMIGROUPS

In order to study rpp semigroups, in particular, some special cases, several facts on (l)-Green’s relations and strongly rpp semigroups are given as some remarks.     

因子拟适当半群(英文)

In this paper,we investigate a class of factorisable IC quasi-adequate semigroups,so-called,factorisable IC quasi-adequate semigroups of type-（H,I）.Some characterizations of factorisable IC quasi-adequate semigroups of type-（H,I） are obtained.In particular,we prove that any IC quasi-adequate semigroup has a factorisable IC quasi-adequate subsemigroups of type-（H,I） and a band of cancellative monoids.     

FINITELY GENERATED COMMUTATIVE ARCHIMEDEAN SEMIGROUPS

In this work commutative Archimedean finitely generated semigroups are characterized in terms of ideal extensions.     

关于序半群的模糊拟理想

In this paper,fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets.Furthermore,we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups and characterize strongly regular ordered semigroups in terms of completely semiprime fuzzy quasi-ideals.Finally,we investigate the characterizations and decompositions of left and right simple ordered semigroups by means of fuzzy quasi-ideals.     

关于Wrpp半群上的Lawson偏序(英文)

In this paper,we introduce Lawson partial order ≤ w on wrpp semigroups.After obtaining some properties of ≤ w,we determine when ≤ w is(left;right) compatible with the multiplication.These results extend and enrich the related results of Lawson and GuoLuo on abundant semigroups,of Guo-Shum on rpp semigroups and of Liu-Guo on wrpp semigroups.     

具有逆断面的局部逆半群

Let S be a locally inverse semigroup with an inverse transversal S°. In this paper, we construct an amenable partial order on S by an R-cone. Conversely, every amenable partial order on S can be constructed in this way. We give some properties of a locally inverse semigroup with a Clifford transversal. In particular, if S is a locally inverse semigroup with a Clifford transversal, then there is an order-preserving bijection from the set of all amenable partial orders on S to the set of all R-cones of S.     

CONTROLLABILITY OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this article, we give sufficient conditions for controllability of some partial neutral functional differential equations with infinite delay. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. The results are obtained using the integrated semigroups theory. An application is given to illustrate our abstract result.     

INVERSE MONOIDS OF GRAPHS

. IntroductionGraph endomorphism and its regularity property have been investigated in some literatures (of. [1--41 for examples). The invertibility is a stronger algebraic property thanregUlarity in semigroup theory. It is commonly agreed that inverse semigroups are the mostpromising class of semigroups for study. In this paper we first present a combinatorial characterization of an inverse monoid of a graph (Theorem 2.3). Then using this we prove thata bipartite graph with an inverse monoi…     

Proportionally modular diophantine inequalities and their multiplicity

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.     

半群的模糊内理想

Abstract The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is a generalization of the quasi-coincidence of a fuzzy point in a fuzzy set. With this new concept, the interval valued （∈, ∈ Vq）-fuzzy interior ideal in semigroups is introduced. In fact, this kind of new fuzzy interior ideals is a generalization of fuzzy interior ideals in semigroups. In this paper, this kind of fuzzy interior ideals and related properties will be investigated. Moreover, the concept of a fuzzy subgroup with threshold is extended to the concept of an interval valued fuzzy interior ideal with threshold in semigroups.