本文選題：(序)半超群 + (模糊)強正則等價關(guān)系��； 參考：《華南理工大學(xué)》2016年博士論文

【摘要】：代數(shù)超結(jié)構(gòu)理論在1934年由Marty首次提出,它是經(jīng)典代數(shù)結(jié)構(gòu)的推廣.上世紀80,90年代,在半群理論的研究背景下,Kepka, Jezec以及Nemec等學(xué)者開展了對半超群結(jié)構(gòu)的研究.半超群是最簡單的一種代數(shù)超結(jié)構(gòu),它是半群概念的推廣.眾所周知,同余關(guān)系是研究半群的一個重要工具.類似地,在半超群上有(強)正則等價關(guān)系.半超群關(guān)于其上正則等價關(guān)系之商結(jié)構(gòu)為半超群,關(guān)于其上強正則等價關(guān)系之商結(jié)構(gòu)為半群.1970年,Koskas提出了半超群上最小的強正則等價關(guān)系,稱為基本關(guān)系,記為β*.模糊集理論于1965年由Zadeh提出.1989年,Nemitz引入集合上模糊關(guān)系的概念.隨后,Samhon介紹并研究了半群上的模糊同余關(guān)系.2000年,Davvaz將模糊關(guān)系理論推廣到半超群上,提出半超群上模糊強正則等價關(guān)系的概念.2008年,Ameri得出半超群上所有強正則等價關(guān)系以及所有模糊強正則等價關(guān)系都構(gòu)成完備格.半群和序關(guān)系相融合可以得到序半群.1993年,Kehayopulu和她的學(xué)生Tsingelis介紹了序半群上擬序的概念,它的作用類似于同余在半群上的作用.隨后,謝祥云借助擬序這一工具清楚地描述了何種同余關(guān)系可以使得相關(guān)商半群還為序半群(非平凡序).2011年,Heidari和Davvaz將這種融合思想應(yīng)用到半超群提出序半超群的概念并對它進行了深入研究.2015年,Davvaz等人提出序半超群上擬序的概念并利用它構(gòu)造出一種強正則等價關(guān)系使得相關(guān)的商結(jié)構(gòu)成為序半群,但他們提出序半超群上是否存在正則等價關(guān)系(非強正則)使得相關(guān)的商結(jié)構(gòu)為序半超群這一問題.本文將在前人研究工作基礎(chǔ)上,針對一些問題對半超群上(模糊)強正則等價關(guān)系和序半超群上(強)序正則等價關(guān)系進行研究,主要研究工作如下.第一章是緒論,主要介紹了半超群上(強)正則等價關(guān)系和序半超群上(強)序正則等價關(guān)系的研究背景、研究現(xiàn)狀以及取得的成果,最后簡述了本文的主要內(nèi)容.第二章研究了半超群上由二元關(guān)系生成的強正則等價關(guān)系以及由模糊關(guān)系生成的模糊強正則等價關(guān)系.作為推論,我們得到半超群上的基本關(guān)系盧*和最小的模糊強正則等價關(guān)系β*f.同時,我們描述了半超群上包含在一個等價關(guān)系中的最大的強正則等價關(guān)系和小于一個模糊等價關(guān)系中的最大的模糊強正則等價關(guān)系.第三章首先介紹了序半超群上(強)序正則等價關(guān)系的概念.然后通過超濾子構(gòu)造出了序半超群上的序半格等價關(guān)系.最后,我們應(yīng)用超理想構(gòu)造出了半超群上的序正則等價關(guān)系,同時也回答了Davvaz等人提出的問題.同時,我們研究了序半超群的直積上的序正則等價關(guān)系.第四章我們首先建立了序半超群上的正規(guī)同態(tài)基本定理.然后介紹了ρ-鏈的概念并應(yīng)用它對序半超群上的強序正則等價關(guān)系進行了刻畫,得出序半超群上所有強序正則等價關(guān)系構(gòu)成完備格.最后,我們研究了序半超群的子集構(gòu)成某些序正則等價類的條件.
[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.

【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O152.7

【相似文獻】

相關(guān)期刊論文 前10條

1 錢宏,羅玉芬;有限集上等價關(guān)系數(shù)目的計算[J];重慶大學(xué)學(xué)報(自然科學(xué)版);1992年03期

2 劉學(xué)鵬;等價關(guān)系的應(yīng)用瑣談[J];臨沂師專學(xué)報;1993年Z1期

3 吳健輝,黃順發(fā);等價關(guān)系作用的認識[J];景德鎮(zhèn)高專學(xué)報;2002年02期

4 黃清蘭;淺談集合上的等價關(guān)系[J];萍鄉(xiāng)高等�？茖W(xué)校學(xué)報;2004年04期

5 劉雙應(yīng);微分方程系漸近等價關(guān)系的一個定理[J];廈門大學(xué)學(xué)報(自然科學(xué)版);1984年04期

6 何瑤;;關(guān)於近世代數(shù)基本概念的表述[J];云南師范大學(xué)學(xué)報(自然科學(xué)版);1986年01期

7 黃天任;n元等價關(guān)系與函數(shù)之間的關(guān)系[J];北京工業(yè)大學(xué)學(xué)報;1987年03期

8 張立昂,耿素云;在多項式等價關(guān)系下P類的結(jié)構(gòu)[J];北京大學(xué)學(xué)報(自然科學(xué)版);1989年03期

9 葛恒林;等價關(guān)系與統(tǒng)計分組[J];財貿(mào)研究;1993年04期

10 沈繼忠;基于邏輯上的等價關(guān)系[J];江西師范大學(xué)學(xué)報(自然科學(xué)版);1997年04期

相關(guān)會議論文 前3條

1 鄧愛民;符曉陵;徐道遠;;混凝土拉、壓損傷的等價關(guān)系研究[A];第十屆全國結(jié)構(gòu)工程學(xué)術(shù)會議論文集第Ⅰ卷[C];2001年

2 梁昌洪;史小衛(wèi);;六端口系統(tǒng)中參數(shù)精度之間的等價關(guān)系和測量范圍分析[A];1995年全國微波會議論文集（下冊）[C];1995年

3 寧佐貴;;模糊控制算法的等價關(guān)系[A];中國工程物理研究院科技年報（1999）[C];1999年

相關(guān)博士學(xué)位論文 前4條

1 谷澤;（序）半超群上的強（序）正則等價關(guān)系[D];華南理工大學(xué);2016年

2 尹志;P(ω)/Fin到ι_p與ι_q之間等價關(guān)系的嵌入[D];南開大學(xué);2013年

3 朱涵;模型獨立的移動演算理論[D];上海交通大學(xué);2009年

4 覃廣平;交互式馬爾可夫鏈：理論與應(yīng)用[D];中國科學(xué)院研究生院（成都計算機應(yīng)用研究所）;2006年

相關(guān)碩士學(xué)位論文 前1條

1 陳鑫;行為等價博弈[D];上海交通大學(xué);2009年

，

本文編號：1854869