| 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 |
| 相關次數: | 點閱:44 下載:3 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
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] D.W. Blackett, Simple and semisimple nearrings, Doctoral Dissertation, Princeton University, 1950.
[2] J.R. Clay, Nearrings: Geneses and Applications, Oxford University Press, 1991.
[3] L.E. Dickson, Definition of a group and a field by independent postulates, Trans. Amer. Math. Soc. 6 (1905), 198-204.
[4] L.E. Dickson, On finite algebras, Nachr. Akad. Wiss. Goettingen (1905), 358-393.
[5] Y. Fong and J.R. Clay, Computer programs for investigating syntactic nearrings of
finite group-semiautomata. Bull. Math. Academia Sinica 12 (1988), 295-304.
[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.
[7] G. Hofer and G. Pilz, Group automata and nearrings. Proc. Conf. Univ.
Klagenfurt (Austria), 153-162, (1982).
[8] J.J. Malone, Nearrings with trivial, multiplications, Amer. Math. Soc. Monthly 74 (1967), 1111-1112.
[9] J.J. Malone and C.G. Lyons, Endomorphism nearrings, Proc. Edin. Math. Soc. 17(1970), 71-78.
[10] H. Neumann, On varieties of groups and their associated nearrings, Math. Z. 65 (1956), 36-69.
[11] G. Pilz, Nearrings, North-Holland / American Elsevier, Amsterdam, First edition, 1977.