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研究生: 謝豐合
Hsieh, Feng-Ho
論文名稱: 遞移函數δ(x,y)= mx + ny產生的句法近環
Syntactic Nearrings generated by the transition function δ(x,y)= mx + ny
指導教授: 方源
Fong, Yuen
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年: 2013
畢業學年度: 101
語文別: 英文
論文頁數: 41
中文關鍵詞: 自動機半自動機群半自動機近環句法近環
外文關鍵詞: Automaton, semiautomaton, group semiautomaton, nearring, syntactic nearring
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  • 在這篇碩士論文中,第一章介紹了近環理論與自動機理論。第二章給出了一個詳盡的刻畫,介紹了以群半自動機所建造而成的句法近環。文中特別給出一類句法近環N(S),此處S=(S_3,S_3,δ),其中δ(x,y)= mx + ny ∀x,y ∈ S_3及m,n為非負整數。

    In this thesis, Chapter1 describes the connections between nearring theory and the theory of automata. In Chapter2, we give a full description of how to construct the structure of a syntactic nearring associated with group semiautomaton. In particular, we give a full description of the syntactic nearrings N(S) where S=(S_3,S_3,δ) with δ(x,y)= mx + ny ∀x,y ∈ S_3 and m,n are non-negative integers.

    1 Introduction and Preliminaries of Nearrings and Automata 7 1.1 Background for Nearrings . . . . . . . . . . . . . . . 7 1.2 Background for Automata . . . . . . . . . . . . . . . 14 2 Syntactic Nearrings 20 2.1 Nearrings Associated with group-semiautomaton . . . . 20 2.2 Syntactic nearrings for some classes of finite non-abelian groups . . . . 25 2.3 Syntactic nearrings N(m;k) on S_3 . . . . . . . . . . 35 Reference 41

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    [6] Y. Fong and W.-F. Ke. Syntactic nearrings of finite group-semiautomata. Proc. Conf. on Ordered Structures and Algebras of Computer Languages, Hong Kong 1991, 31-39. World Scientific, Singapore, 1993.
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    [11] G. Pilz, Nearrings, North-Holland / American Elsevier, Amsterdam, First edition, 1977.

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