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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/22628Full metadata record
| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 李秋坤 | |
| dc.contributor.author | Chih-Whi Chen | en |
| dc.contributor.author | 陳志瑋 | zh_TW |
| dc.date.accessioned | 2021-06-08T04:22:48Z | - |
| dc.date.copyright | 2010-07-06 | |
| dc.date.issued | 2010 | |
| dc.date.submitted | 2010-06-30 | |
| dc.identifier.citation | [1] S.A. Amitsur, Rings of quotients and morita contexts, J. Algebra 17(1971), 273-298.
[2] H. Bass, “The Morita-theorems”, Oregon Lectures, 1962. [3] K.I. Beidar and W.S.Martindale III and A.V. Mikhalev, “Rings with generalized identities”, Marcel Dekker, INC, 1995. [4] A.W. Goldie, The structure of prime rings under ascending chain conditions, Proc. London Math. Sot. 8 (1958), 589-608. [5] A.W. Goldie, Semi-prime rings with maximum condition, Proc. London Math. Sot. 10 (1960), 201-220. [6] N. Jacobson, “PI-algebras”, An introduction. Lecture Notes inMathematics, 441. Springer-Verlag, Berlin-New York, 1975. [7] T.Y. Lam, “Lectures on modules and rings”, Graduate Texts in Mathematics, 189. Springer-Verlag, New York, 1999. [8] T.Y. Lam, “A first course in noncommutative rings. Second edition”, Graduate Texts in Mathematics, 131. Springer-Verlag, New York, 2001. [9] T.-K. Lee, A characterization of left ideals satisfieing polynomial identities, Chinese J. Math., 24(4) (1996), 359-368. [10] W.S. Martindale III, Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576-584. [11] K. Morita, Duality for modules and its application to the theory of rings with minimum conditions, Science Reports of the Tokyo Kyoiku Daigoku Sect. A. 6 (1958), 83-142. [12] C. Procesi and L. Small, Endomorphism Rings of Modules over PI-Algebras, Math. Zeitschr. 106, 178-180 (1968). | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/22628 | - |
| dc.description.abstract | 在本篇論文中，我們延伸 Amitzur 對於 Morita contexts 的研究 [1]。並不假設 Morita contexts 有一致忠實的非奇異左理想，在本文章中我們給出了Morita contexts 是素環的充分必要，並且計算了中心。更進一步地，我們個別刻劃了滿足多項式恆等式與廣義多項式恆等式的Morita contexts，並且計算了多項式階數。我們在文中也給出了在經典Morita contexts 環上的應用。 | zh_TW |
| dc.description.abstract | In this thesis, we continue the study of Morita context in [1]. Without assumption that the Morita contexts has uniformly faithful, non-singular left ideal, here we give the necessary and sufficient condition of the prime Morita contexts, and compute its center.Furthermore, we characterize the Morita contexts to be a polynomial identity ring and generalized polynomial identity ring respectively, and compute its polynomial degree. We also give some applications on classical Morita context. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T04:22:48Z (GMT). No. of bitstreams: 1 ntu-99-R97221007-1.pdf: 434830 bytes, checksum: d262f0af7cd3dd9b552db9dc471b2755 (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | 目 錄
口試委員會審定書……………………………………………………………… i 誌謝………………………………………………………………………………. ii 中文摘要………………………………………………………………………… i ii 英文摘要…………………………………………………………………………. iv 1. Introduction …..……………………………………………………………… 1 2. Primeness ……..……………………………………………………………… 1 3. PI-degree and GPI-rings ...…………………………………………………… 6 4. Primitivity and Simplicity …………………………………………………... 10 5. The associative division algebra ……………………………………………… 11 Reference ..………………………………………………………………………… 12 | |
| dc.language.iso | en | |
| dc.subject | Morita contexts | zh_TW |
| dc.subject | 素環 | zh_TW |
| dc.subject | 多項式恆等式 | zh_TW |
| dc.subject | 廣義多項式恆等式 | zh_TW |
| dc.subject | 多項式階數 | zh_TW |
| dc.subject | 經典Morita contexts | zh_TW |
| dc.subject | prime ring | en |
| dc.subject | Morita contexts | en |
| dc.subject | polynomial degree | en |
| dc.subject | generalized polynomial identity | en |
| dc.subject | polynomial identity | en |
| dc.subject | classical Morita contexts | en |
| dc.title | Morita contexts 環的性質 | zh_TW |
| dc.title | Ring properties of Morita contexts | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 98-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 李白飛,蔡援宗 | |
| dc.subject.keyword | Morita contexts,素環,多項式恆等式,廣義多項式恆等式,多項式階數,經典Morita contexts, | zh_TW |
| dc.subject.keyword | Morita contexts,prime ring,polynomial identity,generalized polynomial identity,polynomial degree,classical Morita contexts, | en |
| dc.relation.page | 13 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2010-06-30 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| Appears in Collections: | 數學系 | |
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| File | Size | Format | |
|---|---|---|---|
| ntu-99-1.pdf Restricted Access | 424.64 kB | Adobe PDF |
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