The Semigroup Structure of Left Clifford Semirings

In this paper,we generalize Clifford semirings to left Clifford semirings by means of the so-called band semirings.We also discuss a special case of this kind of semirings,that is, strong distributive lattices of left rings.  

Group ideals in a semigroup of measures

In this paper we introduce the notion of a group ideal in a semigroup. We shall prove that all group ideals of a compact affine semigroup are convex and dense. This generalizes many results in the literature concerning ideals in semigroups.  

The construction of orthodox super rpp semigroups

We define orthodox super rpp semigroups and study their semilattice decompositions. Standard representation theorem of orthodox super rpp semigroups whose sub-band of idempotents is in the varieties of bands described by an identity with at most three variables are obtained.  

G-Covering Systems of Subgroups for Classes of p-Supersoluble and p-Nilpotent Finite Groups

Let be a class of groups. Given a group G, assign to G some set of its subgroups =(G). We say that is a G-covering system of subgroups for (or, in other words, an -covering system of subgroups in G) if G whenever either =Ø or Ø and every subgroup in belongs to . We find the systems of subgroups in the class of finite soluble groups G which are simultaneously the G-covering systems of subgroups for the classes of p-supersoluble and p-nilpotent groups.  

Interval Valued (∈,∈ ∨q)-Fuzzy Filters of MTL-Algebras

The concepts of interval valued (∈,∈ ∨q)-fuzzy Boolean, MV - and G- filters in a MTL-algebra are introduced. The properties of these generalized fuzzy filters are studied and in particular, the relationships between these fuzzy filters in an MTL-algebra are investigated.  

On radicals of module coalgebras

We introduce the notion of an idempotent radical class of module coalgebras over a bialgebra B. We prove that if R is an idempotent radical class of B-module coalgebras, then every B-module coalgebra contains a unique maximal B-submodule coalgebra in R. Moreover, a B-module coalgebra C is a member of R if, and only if, DB is in R for every simple subcoalgebra D of C. The collection of B-cocleft coalgebras and the collection of H-projective module coalgebras over a Hopf algebra H are idempotent radical classes. As applications, we use these idempotent radical classes to give another proofs for a projectivity theorem and a normal basis theorem of Schneider without assuming a bijective antipode.  

On solubility and supersolubility of some classes of finite groups

Let G be a finite group and H a subgroup of G. Then H is said to be S-permutable in G if HP = PH for all Sylow subgroups P of G. Let HsG be the subgroup of H generated by all those subgroups of H which are S-permutable in G. Then we say that H is S-embedded in G if G has a normal subgroup T and an S-permutable subgroup C such that T ∩ H HsG and HT = C. Our main result is the following Theorem A. A group G is supersoluble if and only if for every non-cyclic Sylow subgroup P of the generalized Fitting subgrou...  

On <Emphasis Type="Italic">U</Emphasis>-orthodox semigroups

As a generalization of an orthodox semigroup in the class of regular semigroups, a type W semigroup was first investigated by El-Qallali and Fountain. As an analogy of the type W semigroups in the class of abundant semigroups, we introduce the U-orthodox semigroups. It is shown that the maximum congruence μ contained in on U-orthodox semigroups can be determined. As a consequence, we show that a U-orthodox semigroup S can be expressed by the spined product of a Hall semigroup W _U and a V-ample semigroup (T,V). This theorem not only generalizes a known result of Hall-Yamada for orthodox semigroups but also generalizes another known result of El-Qallali and Fountain for type W semigroups. This work was supported by National Natural Science Foundation of China (Grant No. 10671151) and Natural Science Foundation of Shaanxi Province (Grant No. SJ08A06), and partially by UGC (HK) (Grant No. 2160123)  

MTL-代数的区间值$(\in,\in \vee q)$-模糊滤子

The concepts of interval valued （∈,∈ ∨q）-fuzzy Boolean, MV - and G- filters in a MTL-algebra are introduced. The properties of these generalized fuzzy filters are studied and in particular, the relationships between these fuzzy filters in an MTL-algebra are investigated.  

Morita equivalence for infinite matrix rings

In this paper, weak distinguished subcategory and distinguished subcategory of modules are introduced. Left(right) local unital rings are particularly considered. Also, representable equivalent functors between categories. By using the replacement techniques of modules, a general theory of Morita equivalence for infinite matrix rings is established. This theory not only extends the classical Morita theory of equivalence from finite matrix rings to infinite matrix rings and also contains some new results which are useful in studying the algebraic structures for infinite matrix rings. Some results of classical Morita theory are included as its special cases.