（序）半超群上的强（序）正则等价关系

发布时间：2018-05-07 01:42

本文选题：(序)半超群 + (模糊)强正则等价关系　；参考：《华南理工大学》2016年博士论文

【摘要】：代数超结构理论在1934年由Marty首次提出,它是经典代数结构的推广.上世纪80,90年代,在半群理论的研究背景下,Kepka, Jezec以及Nemec等学者开展了对半超群结构的研究.半超群是最简单的一种代数超结构,它是半群概念的推广.众所周知,同余关系是研究半群的一个重要工具.类似地,在半超群上有(强)正则等价关系.半超群关于其上正则等价关系之商结构为半超群,关于其上强正则等价关系之商结构为半群.1970年,Koskas提出了半超群上最小的强正则等价关系,称为基本关系,记为β*.模糊集理论于1965年由Zadeh提出.1989年,Nemitz引入集合上模糊关系的概念.随后,Samhon介绍并研究了半群上的模糊同余关系.2000年,Davvaz将模糊关系理论推广到半超群上,提出半超群上模糊强正则等价关系的概念.2008年,Ameri得出半超群上所有强正则等价关系以及所有模糊强正则等价关系都构成完备格.半群和序关系相融合可以得到序半群.1993年,Kehayopulu和她的学生Tsingelis介绍了序半群上拟序的概念,它的作用类似于同余在半群上的作用.随后,谢祥云借助拟序这一工具清楚地描述了何种同余关系可以使得相关商半群还为序半群(非平凡序).2011年,Heidari和Davvaz将这种融合思想应用到半超群提出序半超群的概念并对它进行了深入研究.2015年,Davvaz等人提出序半超群上拟序的概念并利用它构造出一种强正则等价关系使得相关的商结构成为序半群,但他们提出序半超群上是否存在正则等价关系(非强正则)使得相关的商结构为序半超群这一问题.本文将在前人研究工作基础上,针对一些问题对半超群上(模糊)强正则等价关系和序半超群上(强)序正则等价关系进行研究,主要研究工作如下.第一章是绪论,主要介绍了半超群上(强)正则等价关系和序半超群上(强)序正则等价关系的研究背景、研究现状以及取得的成果,最后简述了本文的主要内容.第二章研究了半超群上由二元关系生成的强正则等价关系以及由模糊关系生成的模糊强正则等价关系.作为推论,我们得到半超群上的基本关系卢*和最小的模糊强正则等价关系β*f.同时,我们描述了半超群上包含在一个等价关系中的最大的强正则等价关系和小于一个模糊等价关系中的最大的模糊强正则等价关系.第三章首先介绍了序半超群上(强)序正则等价关系的概念.然后通过超滤子构造出了序半超群上的序半格等价关系.最后,我们应用超理想构造出了半超群上的序正则等价关系,同时也回答了Davvaz等人提出的问题.同时,我们研究了序半超群的直积上的序正则等价关系.第四章我们首先建立了序半超群上的正规同态基本定理.然后介绍了ρ-链的概念并应用它对序半超群上的强序正则等价关系进行了刻画,得出序半超群上所有强序正则等价关系构成完备格.最后,我们研究了序半超群的子集构成某些序正则等价类的条件.
[Abstract]:The theory of algebraic superstructure was first proposed by Marty in 1934. It is the generalization of the classical algebraic structure. In the 80,90 age of the last century, under the background of the semigroup theory, the scholars of Kepka, Jezec and Nemec have carried out the study of semi superstructure. Semi supergroup is the simplest kind of algebraic superstructure, which is the generalization of the semigroup concept. It is well known that The congruence relation is an important tool for the study of semigroups. Similarly, there are (strong) regular equivalence relations on semi super groups. The quotient structure of semi Super Group on its regular equivalence relation is semi super group, and the quotient structure of its strong regular equivalence relation is semigroup.1970 years, and Koskas puts forward the minimum strong regular equivalence relation on semi super group, which is called the basic. The relationship is recorded as beta *. In 1965, the fuzzy set theory was proposed by Zadeh for.1989 years and Nemitz introduced the concept of fuzzy relations on the set. Then, Samhon introduced and studied the fuzzy congruence relation on the semigroup for.2000 years. Davvaz extended the fuzzy relation theory to semi super group, and proposed the concept of semi Super Group on the fuzzy strong regular equivalence relation for.2008 years, Ameri obtained Ameri. All strong regular equivalence relations and all fuzzy strong regular equivalents constitute complete lattice. The fusion of semigroups and order relations can get order semigroups.1993 years. Kehayopulu and her student Tsingelis introduce the concept of order in order semigroup, its function is similar to the function of congruence on semigroups. Then, Xie Xiangyun uses the help of the semigroup. The congruence tool clearly describes what congruence relation can make related quotient semigroups also used in order Semigroups (non trivial order).2011 years, Heidari and Davvaz to apply the concept of semi super group to the concept of ordered semi super group and further study it for.2015 years. Davvaz et al. Put forward the concept of order semi super group. It constructs a strong regular equivalence relation that makes the related quotient structures become order semigroups, but they propose that there is a regular equivalence relation (non strong regular) in order half super group (non strong regular), which makes the related quotient structure be ordered semi super group. The first chapter is the introduction, which mainly introduces the research background of the semi super group (strong) regular equivalence relation and the order semi super group (strong) order regular equivalence relation, the research status and the achievements. Finally, the main contents of this paper are briefly described. Second In this chapter, we have studied the strong regular equivalence relation generated by the semi super group by the two element relation and the fuzzy strong regular equivalence relation generated by the fuzzy relation. As the inference, we get the basic relation of the semi super group and the minimum fuzzy strong regular equivalence relation beta *f.. The large strong regular equivalence relation and the maximum fuzzy strong regular equivalence relation in the fuzzy equivalence relation. Third Zhang Shouxian introduces the concept of the ordered regular equivalence relation in order semi super group. Then, the order semilattice equivalence relation on the ordered semi super group is constructed by the ultrafiltration. Finally, we use the super ideal to construct Ban Chao. The order regular equivalence relation on the group also answers the questions raised by Davvaz et al. At the same time, we study the order regular equivalence relation on the direct product of ordered semigroups. In the fourth chapter, we first set up the basic theorem of normal homomorphism on the ordered semigroup. Then we introduce the concept of the Rho chain and apply it to the strong order regularity on the ordered semigroup. The valence relation is depicted, and the complete lattice of all the strong order regular equivalence relation on the ordered semi super group is obtained. Finally, we study the condition of the order regular equivalence class of the subsets of order semi super group.

【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O152.7

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