首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 140 毫秒
1.
具有拟理想正则*-断面的正则半群   总被引:4,自引:1,他引:3  
李勇华 《数学进展》2003,32(6):727-738
本文提出了具有正则*-断面正则半群的概念,所给出的例子表明具有拟理想正则*-断面的正则半群类真包含了具有拟理想逆断面的正则半群类和正则*-半群类;最后刻画了具有拟理想正则*-断面的正则半群的结构.  相似文献   

2.
喻秉钧 《中国科学A辑》1990,33(11):1154-1161
称π正则半群S为严格π正则的,若其正则元集RegS是S的理想且为完全正则半群.本文给出了这类半群的一个结构定理.由该定理可推出文献[3,6]的两个结构定理并可简化文献[7]的一个结构定理.  相似文献   

3.
半群断面的同构   总被引:1,自引:0,他引:1  
陈建飞  芮昌祥 《数学进展》2002,31(4):355-362
我们首先证明,若S^*,S^o是正则半群S的两个纯正断面,σ^*,σ^o分别是S^*,S^o上的最小逆半群同余,则商半群S^*/σ^o同构。作为上述结论的一个推论,重新获得:含逆断面的正则半群的所有逆断面均同构。关于富足半群我们证明了:满足正则性条件的富足半群若含有似理想恰当断面,则其所有拟理想恰当断面均同构。  相似文献   

4.
关于Fuzzy完全正则半群   总被引:3,自引:3,他引:0  
本文先引入Fuzzy左(Fuzzy右)正则半群的概念,进而讨论Fuzzy左(Fuzzy右)正则半群以及Fuzzy完全正则半群中Fuzzy理想的一些代数性质。  相似文献   

5.
许新斋  曹勇  李秀明 《数学研究》2007,40(2):139-142
给出了正则交换序半群的与素理想结构有关的若干性质,还给出了为有限个主理想的并的交换序半群类中的诺特性,阿基米德性,正则性以及有限生成性之间的一些关系。  相似文献   

6.
李勇华 《数学进展》2006,35(5):607-614
设S是一个正则半群,如果存在一个S的子半群S~*及上的一元运算*满足条件:(1)(?)x∈S,x~*∈S~*∩V(x);(2)(?)x∈S~*,(x~*)~*=x;(3)(?)x,y∈S,(x~*y)~*=y~*x~(**),(xy~*)~*=y~(xx)x~*则称S~*是S的一个正则*_-断面.本文刻画了具有正则*_-断面的正则半群的结构。  相似文献   

7.
朱凤林  刘卫江 《数学研究》2001,34(1):105-108
讨论了具有E-逆断面的正则半群的性质;并给出了具有E-逆断面的正则半群的一种结构定理。  相似文献   

8.
本文证明了半群S是一个具有左中心幂等元的弱L-正则半群,当且仅当S为H-左可消幺半群和右零带直积的强半格,并借助具有中心幂等元的弱L-正则半群和右正规带建立了半群S的强织积结构.  相似文献   

9.
本文主要研究模糊正则子半群的度量问题,利用模糊正则子半群度讨论了正则半群的模糊子集是模糊正则半群的程度。首先,文章通过[0,1]上的蕴含给出了模糊正则子半群度的定义。其次,利用正则半群模糊集的(强)水平集得到了模糊正则子半群度的等价刻画。最后,讨论了任意多个模糊子集的交、直积的模糊正则子半群度以及正则半群的模糊子集在同态映射下像与原像的模糊正则子半群度的性质。  相似文献   

10.
介绍序半群中具有边界值(α,β)的直觉模糊左理想和直觉模糊双理想的概念,对其性质进行了探讨,并通过有边界值(α,β)的直觉模糊左理想和直觉模糊双理想,对左正则和正则序半群的特征进行了研究.  相似文献   

11.
In this paper we study commutative semigroups whose every homomorphic image in a group is a group. We find that for a commutative semigroup S, this property is equivalent to S being a union of subsemigroups each of which either has a kernel or else is isomorphic to one of a sequence T0, T1, T2, ... of explicitly given, countably infinite semigroups without idempotents. Moreover, if S is also finitely generated then this property is equivalent to S having a kernel.  相似文献   

12.
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   

13.
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   

14.
Let S be a semigroup whose set of proper right congruences form a tree. The main theorem is a characterization of those semigroups having this property. In this characterization we draw on the results of Schein and Tamura for commutative semigroups and Kozhukhov for left chain semigroups and Hitzel for nilpotent semigroups. The interested reader should also see the work of Nagy on -semigroups.  相似文献   

15.
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   

16.
17.
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   

18.
Guo 《Semigroup Forum》2008,66(3):368-380
Abstract. 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   

19.
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   

20.
The purpose of this paper is to develop a general theory of semilattice decompositions of semigroups from the point of view of obtaining theorems of the type: A semigroup S has propertyD if and only if S is a semilattice of semigroups having property β. As such we are able to extend the theories of Clifford [3], Andersen [1], Croisot [5], Tamura and Kimura [14], Petrich [9], Chrislock [2], Tamura and Shafer [15], Iyengar [7] and Weissglass and the author [10]. The root of our whole theory is Tamura's semilattice decomposition theorem [12, 13]. Of this, we give a new proof. The results of this paper were obtained by the author between January and July of 1971, while an undergraduate at the University of California, Santa Barbara.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号