关于具有某种断面的半群的若干研究

兰州大学机构库 >数学与统计学院

	关于具有某种断面的半群的若干研究
Alternative Title	Some studies on semigroups with some kind of transversals
	孔祥军
Thesis Advisor	罗彦锋
	2011-06-03
Degree Grantor	兰州大学
Place of Conferral	兰州
Degree Name	博士
Keyword	正则半群逆半群纯正半群富足半群恰当半群拟恰当半群逆断面纯正断面恰当断面拟恰当断面
Abstract	本文主要研究具有纯正断面的正则半群与分别具有恰当断面和拟恰当断面的富足半群,共分六章.第一章为本文的引言和预备知识.第二章引入左单纯正断面的概念.给出例子说明左单纯正断面是拟理想纯正断面的真推广.研究了具有左单纯正断面的正则半群并给出了这类半群的一个结构定理.第三章引入 ~$S$-纯正断面的概念.给出例子说明~$S$-纯正断面是左单纯正断面的真推广. 给出了具有~$S$-纯正断面的正则半群的一个结构定理. 作为此结构定理的应用,得到了具有拟理想纯正断面的正则半群与具有逆断面的正则半群的结构定理.第四章探讨富足半群的恰当断面之间的关系. 证明了若富足半群 ~$S$ 具有一个可乘恰当断面, 则 ~$S$ 的任一拟理想恰当断面是可乘的. 引入并研究弱可乘恰当断面,得到恰当断面是可乘的与弱可乘的和拟理想的关系.研究了富足半群的拟理想恰当断面的乘积问题.第五章研究具有~$S$-恰当断面的富足半群.用两种不同的方法给出了分别具有拟理想~$S$-恰当断面和~$S$-恰当断面的富足半群的结构.第六章研究具有可乘拟恰当断面的富足半群.得到了具有可乘拟恰当断面的富足半群的若干性质,并给出了这类半群的一个新的结构定理.
Other Abstract	This thesis consists of six chapters. We mainly investigate regular semigroups with orthodox transversals and abundant semigroups with adequate transversals and quasi-adequate transversals respectively.The first chapter is introduction and preliminaries.In Chapter 2, the concept of left simplistic orthodox transversals is introduced. An example is given to demonstrate that left simplistic orthodox transversals are proper generalizations of quasi-ideal orthodox transversals.Regular semigroups with left implistic orthodox transversals are explored and a structure theorem for this class of semigroups is also established.In Chapter 3, the concept of $S$-orthodox transversals is introduced. An example is given to demonstrate that $S$-orthodox transversals are proper generalizations of left simplistic orthodox transversals. A structure theorem for regular semigroups with $S$-orthodox transversals is established. As applications of this structure theorem, the structures of regular semigroups with quasi-ideal orthodox transversals and inverse transversals respectively are acquired. In Chapter 4, relationship between the adequate transversals of an abundant semigroup is explored. It is proved that if an abundant semigroup $S$ has a multiplicative adequate transversal, then every quasi-ideal adequate transversal of $S$ is multiplicative. Weakly multiplicative adequate transversals are introduced and explored. The connection of an adequate transversal between the properties of being multiplicative, weakly multiplicative and a quasi-ideal is obtained. The product of quasi-ideal adequate transversals of an abundant semigroup is investigated. In Chapter 5, abundant semigroups with $S$-adequate transversals are studied. The structures of abundant semigroups with quasi-ideal $S$-adequate transversals and $S$-adequate transversals respectively are established by means of two methods. In Chapter 6, abundant semigroups with multiplicative quasi-adequate transversals are studied. Some properties of abundant semigroups with multiplicative quasi-adequate transversals are characterized. A new structure theorem for this class of semigroups is also established.
URL	查看原文
Language	中文
Document Type	学位论文
Identifier	https://ir.lzu.edu.cn/handle/262010/225352
Collection	数学与统计学院
Recommended Citation GB/T 7714	孔祥军. 关于具有某种断面的半群的若干研究[D]. 兰州. 兰州大学,2011.

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