發(fā)布時(shí)間：2018-01-12 13:32

  本文關(guān)鍵詞：關(guān)于半環(huán)正則性的研究　出處：《蘇州科技大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 半環(huán) 正則半環(huán) 單半環(huán) 半環(huán)半直積 圈積

【摘要】：半環(huán)理論是代數(shù)學(xué)的重要組成部分。在半環(huán)理論研究的眾多方面中,正則性及其特殊情況的研究是該領(lǐng)域研究的熱點(diǎn)之一。半環(huán)理論已在形式語言、信息科學(xué)及自動(dòng)機(jī)理論等領(lǐng)域得到了較為廣泛的應(yīng)用。本文利用半群的代數(shù)理論和方法,研究了半環(huán)半直積,圈積的正則性,給出了半環(huán)半直積,圈積及其幾種特殊情形的正則性的刻畫。全文共分為四章。第一章緒論,簡要論述國內(nèi)外有關(guān)半環(huán)理論發(fā)展的概況及與課題相關(guān)的研究背景和意義,并介紹本文的主要研究內(nèi)容和所做的工作。第二章半環(huán)的正則性。首先介紹了本文所需的主要概念和結(jié)果,然后研究半環(huán)的正則性,給出半環(huán)為正則半環(huán)的等價(jià)刻畫。第三章半環(huán)的半直積。引入半環(huán)半直積的概念,研究半環(huán)半直積的正則性,給出了半環(huán)半直積正則性、逆性和純整性的特征。得到了若干相關(guān)結(jié)果。第四章半環(huán)半直積的應(yīng)用。引入半環(huán)圈積正則的概念,討論了幾類特殊的正則半環(huán)圈積的性質(zhì)。
[Abstract]:Semiring theory is an important part of algebra. Among the many aspects of semiring theory, regularity and its special situation are one of the hotspots in this field. Semirings theory is already in formal language. Information science and automata theory have been widely used. In this paper, we study the regularity of semidirect product and cycle product by using algebraic theory and method of semigroup, and give semircular semi-direct product. This paper is divided into four chapters. Chapter one is an introduction to the development of semiring theory at home and abroad as well as the research background and significance related to the subject. In chapter 2, the regularity of semirings is introduced. Firstly, the main concepts and results of this paper are introduced, and then the regularity of semirings is studied. This paper gives the equivalent characterization of semirings being regular semirings. In Chapter 3, the semi-direct product of semirings is introduced. The regularity of semi-direct products of semirings is studied, and the regularity of semi-direct products of semirings is given. Some related results are obtained. In Chapter 4th, we introduce the concept of semiring cycle product regularity, and discuss the properties of some special regular semirings product.
【學(xué)位授予單位】：蘇州科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O153.3

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