w-Stability and Clifford w-Regularity of Polynomial Rings

We investigate the transfer of w-stability and Clifford w-regularity from a domain D to the polynomial ring D[X]. We show that these two properties pass from D to D[X] when D is either integrally closed or it is Mori and w-divisorial.     

Abel正则球与完全正则半群

本文分别讨论了关于结合环和半群的二个定理，并且由结合环的这二个定理推出了如下准则：结合环Ｒ是Ａｂｅｌ正则的，当且仅当Ｒ的每个拟理想是正则环．     

On a Class of Subdirect Products of Left and Right Clifford Semigroups

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.     

具有Clifford断面的正则纯正半群

给出了具有Clifford断面的右正规纯正半群的等价刻画,得到了具有Clifford断面的正则纯正半群的次直积分解,证明了具有Clifford断面的正则纯正半群一定是正则纯正群．     

Characterizations of Clifford semigroup digraphs

This paper characterizes directed graphs which are Cayley graphs of strong semilattices of groups and, in particular, strong chains of groups, i.e. of completely regular semigroups which are also called Clifford semigroups.     

一类Clifford半群的刻画

G是一个群,I是一个指标集.令CG=G×I={(g,i):g∈G,i∈I};(a,i)(b,j)=(ab,k)with k=min{i,j}则CG是一个半群.事实上,CG是Clifford半群,并且CG代表了一类特殊的Clifford半群.     

半格序Clifford半群

证明了每一个半格序Clifford半群都能嵌入到其加法半群的半格序自同态半群当中;给出了同余单的半格序Clifford半群所具有的几种形式,得到了自然半格序零群是仅有的次直不可约自然半格序Clifford半群.     

E-自反逆半群上的Clifford同余

研究E-自反逆半群上的Clifford同余.本文中的结果是James[1],McAlister[2],Petrich[3]和Reilly[4]等人关于E-酉逆半群上的相应同余定理在E-自反逆半群上的自然推广.     

The Closed Subsemigroups of a Clifford Semigroup

In this paper we study the closed subsemigroups of a Clifford semigroup. shown that{∪- αεY＇ Gα, [ Y＇ ε P（Y）} is the set of all closed subsemigroups of It is a Clifford semigroup S = {Y; Gα; Фα,β}, where Y＇- denotes the suhsemilattice of Y generated by Y＇. In particular, G is the only dosed subsemigroup of itself for a group G and each one of subsemilattiees of a semilattiee is closed. Also, it is shown that the semiring P（S） is isomorphic to the semiring P（Y） for a Clifford semigroup S = [Y; Gα; Фα,β].     

The Closed Subsemigroups of a Clifford Semigroup

In this paper we study the closed subsemigroups of a Clifford semigroup. It is shown that {∪α∈Y′ Gα | Y′∈ P(Y) } is the set of all closed subsemigroups of a Clifford semigroup S = [Y; Gα; ?α, β], where Y′denotes the subsemilattice of Y generated by Y′. In particular, G is the only closed subsemigroup of itself for a group G and each one of subsemilattices of a semilattice is closed. Also, it is shown that the semiring P(S) is isomorphic to the semiring P(Y) for a Clifford semigroup S = [Y; Gα; ?α, β].     

右Clifford左商半群

本文讨论了右Ｃｌｉｆｆｏｒｄ左商半群．利用所谓的可适对刻划了右Ｃｌｉｆｆｏｒｄ半群中的左次半群,因此扩展了商半群的研究范围．     

Clifford Extensions

Formulating the construction of Clifford algebras, we introduce the notion of Clifford extensions and show that Clifford extensions are Frobenius extensions. Consequently, Clifford extensions of Auslander–Gorenstein rings are Auslander–Gorenstein rings.     

空间最佳N冲击过渡的伴随系统积分

推出了发动机点火过程中空间最佳N冲击过渡(时间任意)的伴随系统在所选5维相空间中的积分。     

Clifford拟正则半群的半直积

给出了两个半群S和T的半直积是Clifford拟正则半群的充要条件，同时还讨论了S和T^e半直积的结构，其中T^e＝{t^e|Vt∈T,Vc∈E（S）}。     

关于半群环与群环的链条件的等价性

给出了将半群环的链条件转化为群环的链条件的一个定理,并由此将［１］中的结果推广到半群环的情形．     

左Clifford拟正则半群的半直积和圈积

在半群不含单位元的情况下,给出了两个半群的半直积和圈积是左Clifford拟正则半群的充分必要条件.     

Fuzzy Order Filters in Adjoint Semigroups of BCK-Algebras

In this paper, we introduce the notion of fuzzy order filters in adjoint semigroups of BCK-algebras. We prove that there is a bijection between the fuzzy ideals of BCK-algebras X and the fuzzy order filters in the adjoint semigroup M(X) of X.AMS Subject Classification (2000) 06F35 03G25 20M10     

Radical Semigroup Rings and the Thue--Morse Semigroup

Let R be an associative ring with unit, let S be a semigroup with zero, and let RS be a contracted semigroup ring. It is proved that if RS is radical in the sense of Jacobson and if the element 1 has infinite additive order, then S is a locally finite nilsemigroup. Further, for any semigroup S, there is a semigroup T S such that the ring RT is radical in the Brown--McCoy sense. Let S be the semigroup of subwords of the sequence abbabaabbaababbab..., and let F be the two-element field. Then the ring FS is radical in the Brown--McCoy sense and semisimple in the Jacobson sense.     

关于GP-V-环与强正则环的刻划

The purpose of this paper is to characterize strongly regular rings via MERT rings and weakly one-sided ideals. Many important equivalent conditions on strongly regular rings are shown.     

Some relations on completely regular semigroups

A semigroup S is called a Clifford semigroup if it is completely regular and inverse. In this paper, some relations related to the least Clifford semigroup congruences on completely regular semigroups are characterized. We give the relation between Y and ξ on completely regular semigroups and get that Y ^* is contained in the least Clifford congruence on completely regular semigroups generally. Further, we consider the relation Y ^*, Y, ν and ε on completely simple semigroups and completely regular semigroups. This work is supported by Leading Academic Discipline Project of Shanghai Normal University, Project Number: DZL803 and General Scientific Research Project of Shanghai Normal University, No. SK200707.