偏序半环的偏序扩张

【作者】 邵海琴；

【导师】 赵宪钟；

【作者基本信息】 西北大学 ， 基础数学， 2007， 硕士

【摘要】 偏序代数理论，是重要的代数学分支，许多专家学者对其进行了深入细致的研究。本文主要研究了偏序半环的偏序扩张和有限全序扩张，并得到了一些新的结果。本文的主要内容分为三章。第一章介绍了本文的选题背景及课题意义，介绍了偏序半环、拟序、拟链、半格与格及其同态与序同态等概念与有关基础知识。第二章以偏序半环的偏序扩张为中心，引入了偏序半环的半拟序与半拟链的概念并得到了它们的一些基本性质，给出了偏序半环的偏序扩张的构造方法，得到了偏序半环能够偏序扩张的充分条件。第三章以偏序半环的有限全序扩张为中心，给出了偏序半环的有限全序扩张的概念和偏序半环能进行有限全序扩张的充分必要条件。更多还原

【Abstract】 Ordered algebric theory is a very important branch of algebra. Many experts and scholars have investigated it thoroughly and painstakingly. In this paper, we mainly study extensions of partial order and finitely totally order for partially ordered semirings, and obtain some new results.This dissertation can be divided into three parts. The first chapter, we introduce the history of semigroups, semirings, partially ordered semigroups, partially ordered semirings. we emphasize that the thesis is mainly concerned with several important papers arising in extensions of partial order for ordered algebraic theory. Also, we introduce the basic notions and results of partially ordered semirings, pseudoorder, pseudochain, semi-lattices, lattices, isotonic homomorphism and homomorphism of them. The second chapter, we introduce the notions of semi-pseudoorderσand semi-pseudochain modσon the partially ordered semirings and give some basic properties of them. we also give a constructive method of extensions of partial order for partially ordered semirings. Besides, we get sufficient condition of extensions of partial order for partially ordered semirings by semi-pseudochain modσ, and obtain some interesting results. In chapter 3. we give the notion of extensions of finitely totally order for partially ordered semirings, Besides, we discuss sufficient and necessary conditions on extensions of finitely totally order for partially ordered semirings.更多还原