| dc.contributor.advisor | 陳天進 | zh_TW |
| dc.contributor.author (Authors) | 陳薇 | zh_TW |
| dc.contributor.author (Authors) | Chen, Wei | en_US |
| dc.creator (作者) | 陳薇 | zh_TW |
| dc.creator (作者) | Chen, Wei | en_US |
| dc.date (日期) | 2008 | en_US |
| dc.date.accessioned | 8-Dec-2010 11:48:34 (UTC+8) | - |
| dc.date.available | 8-Dec-2010 11:48:34 (UTC+8) | - |
| dc.date.issued (上傳時間) | 8-Dec-2010 11:48:34 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0095751014 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/49454 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學研究所 | zh_TW |
| dc.description (描述) | 95751014 | zh_TW |
| dc.description (描述) | 97 | zh_TW |
| dc.description.abstract (摘要) | 在這篇論文裡, 我們探討體中之賦值的一般理論. 最主要的, 我們證明了多個賦值等價條件. 進而我們探討p進位數體中的分析, 得到ㄧ些新的現象與例子. | zh_TW |
| dc.description.abstract (摘要) | In this thesis, we study some general theory of valuations on a field. Especially, we obtain several equivalent conditions on the equivalence of two valuations on a field, some of them are new in the literature. Moreover, we study the $p$-adic analysis on the p-adic number fields and obtain some new phenomena and examples. | en_US |
| dc.description.tableofcontents | 謝辭-------------------------------------------------------iAbstract-------------------------------------------------iii中文摘要---------------------------------------------------iv1 Introduction---------------------------------------------12 General Theory of Valuations-----------------------------23 Topology of Valuated Fields-----------------------------164 Completion of Valuations--------------------------------245 Equivalence of Valuations-------------------------------346 p-Adic Number Field and Arithmetic----------------------437 p-Adic Series-------------------------------------------52References------------------------------------------------59 | zh_TW |
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| dc.format.mimetype | application/pdf | - |
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| dc.format.mimetype | application/pdf | - |
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| dc.format.mimetype | application/pdf | - |
| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0095751014 | en_US |
| dc.subject (關鍵詞) | p進位數 | zh_TW |
| dc.subject (關鍵詞) | 賦 | zh_TW |
| dc.subject (關鍵詞) | p-adic | en_US |
| dc.subject (關鍵詞) | valuation | en_US |
| dc.subject (關鍵詞) | valuated field | en_US |
| dc.title (題名) | 探討p進位數之分析 | zh_TW |
| dc.title (題名) | On some p-adic analysis | en_US |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | References | zh_TW |
| dc.relation.reference (參考文獻) | [1]T. M. Apostol, Mathematical Analysis, Addion-Wesley, 1974. | zh_TW |
| dc.relation.reference (參考文獻) | [2]G. Bachman, Introduction to p-Adic Numbers and Valuation Theory, Academic Press, New York and London, 1964. | zh_TW |
| dc.relation.reference (參考文獻) | [3]J. W. S. Cassels, Local Fields, Cambridge University Press, Cambridge, 1986. | zh_TW |
| dc.relation.reference (參考文獻) | [4]J. B. Fraleigh, A First Course in Abstract Algebra, 7th | zh_TW |
| dc.relation.reference (參考文獻) | Ed., Addion-Wesley, 2003. | zh_TW |
| dc.relation.reference (參考文獻) | [5]I. N. Herstein, Topics in Algebra, New York: Blaisdell, | zh_TW |
| dc.relation.reference (參考文獻) | 1964. | zh_TW |
| dc.relation.reference (參考文獻) | [6]S. Katok, Real and $p$-Adic Analysis Course Notes, http://www.math.psu.edu/katok_s/pub/p-adic.pdf, 2001. | zh_TW |
| dc.relation.reference (參考文獻) | [7]N. Koblitz, p-Adic Numbers, p-Adic Analysis, and Zeta-Functions, Springer-Verlag, Berlin, Heidelberg, New York, | zh_TW |
| dc.relation.reference (參考文獻) | 2nd Ed., 1984. | zh_TW |
| dc.relation.reference (參考文獻) | [8]K. Mahler, p-Adic Numbers and Their Functions, Cambridge | zh_TW |
| dc.relation.reference (參考文獻) | Press, 1973. | zh_TW |
| dc.relation.reference (參考文獻) | [9]A. M. Robert, A Course in p-Adic Analysis, Springer-Verlag, Berlin, Heidelberg, New York, 2000. | zh_TW |
| dc.relation.reference (參考文獻) | [10]W. H. Schikoff, Ultrametric Calculus, An Introduction to | zh_TW |
| dc.relation.reference (參考文獻) | p-Adic Analysis, Cambridge Studies in Adv. Math.4, Cambridge | zh_TW |
| dc.relation.reference (參考文獻) | University Press, 1984. | zh_TW |
