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1.
具有左单S-恰当断面的富足半群的结构(英文)   总被引:1,自引:0,他引:1  
王蓓  孔祥军 《数学进展》2012,(5):554-564
本文得到具有左单恰当断面的富足半群的进一步刻画.推广并丰富了Blyth和AlmeidaSantos于1996年得到的关于左单逆断面及两位作者分别于2008年与2010年得到的关于恰当断面的相关结果.建立了具有左单S-恰当断面的富足半群的结构.  相似文献   

2.
本文首先研究了具有可消模断面的拟恰当半群的结构,然后给出了用可消模断面的拟恰当半群构造具有CO-恰当断面富足半群的方法.  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.
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   

5.
具有某种断面的半群的研究进展   总被引:1,自引:0,他引:1  
汪立民 《数学进展》2002,31(6):485-494
本文综述了几类具有特殊断面的半群的近期研究结果。在介绍逆半群和正则半群的一般结构之后,概述了具有逆断面的正则半群的结构和同余格的研究成果。总结了作为逆断面的推广的可裂断面,纯正断面,正则^*-断面和恰当断面。提出了可以进一步研究的重要的问题。  相似文献   

6.
在强E-右拟富足半群上定义关系γ,得到γ的性质.利用关系γ,主要研究了一类拟富足半群一完备右拟富足半群,得出这类半群的结构定理.另外,给出这类半群的另一种刻画.  相似文献   

7.
本文给出了带正则*-断面的正则半群的若干性质,获得了带拟理想正则*-断面的正则半群的一个构造方法.利用这一构造定理,考虑了这类半群上的同余.  相似文献   

8.
一个逆半群如果只有一个D-类,则称为双单逆半群.一个型A半群只有一个D*-类和一个正则D-类,则称为*-双单型A半群.本文采用McAlister的刻画双单逆半群的方法([Proc.London Math.Soc.,1974,28(2):193-221]),用一致半格和可消幺半群建立了*-双单型A半群的结构.  相似文献   

9.
本文研究含左正则lpp-断面的lpp-半群的结构.特别地,给出了合右理想左正则lpp-断面的lpp-半群的一个结构.另外,还把这个结构用于一些特殊情况。  相似文献   

10.
对拟内正则序半群给出了在理想和格林关系理论方面的若干刻划。这些刻划推广和扩充了由N.Kehayopulu给出的对内正则序半群的刻划.  相似文献   

11.
The aim of this article is to study abundant semigroups with generalized adequate transversals. We obtain some properties of such semigroups and give, in particular, a construction of the class of abundant semigroups with quasi-ideal generalized adequate transversals. Finally, we apply this construction to some special cases.  相似文献   

12.
in this paper, new characteristic properties of strongly regular rings are' given.Relations between certain generalizations of duo rings are also considered. The followingconditions are shown to be equivalent: (1) R is a strongly regular ring; (2) R is a left SFring such that every product of two independent closed left ideals of R is zero; (3) R is aright SF-ring such that every product of two independent closed left ideals of R is zero; (4)R is a left SF-ring whose every special left annihilator is a quasi-ideal; (5) R is a right SFring whose every special left annihilator is a quasi-ideal; (6) R is a left SF-ring whose everymaximal left ideal is a quasi-ideal; (7) R is a right SF-ring whose every maximal left ideal isa quasi-ideal; (8) R is a left SF-ring such that the set N(R) of all nilpotent elements of R isa quasi-ideal; (9) R is a right SF-ring such that N(R) is a quasi-ideal.  相似文献   

13.
The product of quasi-ideal adequate transversals of an abundant semigroup   总被引:1,自引:0,他引:1  
An inverse transversal of a regular semigroup S is an inverse subsemigroup that contains precisely one inverse of each element of S. This concept was first introduced by Blyth and McFadden and generalized to an adequate transversal in the abundant case by El-Qallali. In this paper we show that the product of any two quasi-ideal adequate transversals of an abundant semigroup S which satisfy the regularity condition is a quasi-ideal adequate transversal of S. Furthermore, all adequate transversals of S form a rectangular band.  相似文献   

14.
《代数通讯》2013,41(4):1779-1800
ABSTRACT

The aim of this paper is to study idempotent-connected abundant semigroups which are disjoint unions of quasi-ideal adequate transversals. After obtaining some characterizations of such semigroups, we establish the structure of this class of semigroups. In addition, we also consider several special cases.  相似文献   

15.
We provide a new and much simpler structure for quasi-ideal adequate transversals of abundant semigroups in terms of spined products, which is similar in nature to that given by Saito in Proc. 8th Symposium on Semigroups, pp. 22–25 (1985) for weakly multiplicative inverse transversals of regular semigroups. As a consequence we deduce a similar result for multiplicative transversals of abundant semigroups and also consider the case when the semigroups are in fact regular and provide some new structure theorems for inverse transversals.  相似文献   

16.
Let R be an associative ring with 1 and $Y \ne R$ a quasi-ideal of R. Set $T_2(R,Y)={diag(u,v)a^{1,2}b^{2,1}c^{1,2}:a+c,b\in Y,u,v\in GL_1R,and v^{-1}au-a,uav^{-1}-a\in Y for all a\in R}$.It is proved that if R satisfies 2-fold condition, then $[E_2R,T_2(R,Y)]\subset E_2(R,Y)\subset T_2(R,Y)$; and if R satisfies 6-fold condition, then $E_2(R,Y)=[E_2R,E_2(R,Y)]=[E_2R,T_2(R,Y)]$ and the sandwich theorem holds.  相似文献   

17.
研究了每一个极大的右理想是拟理想的右SF-环的正则性,得到了右SF-环是正则环的一些新的刻画,推广了一些已知的结论.  相似文献   

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