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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 李秋坤 | |
| dc.contributor.author | Kun-Shan Liu | en |
| dc.contributor.author | 劉崑山 | zh_TW |
| dc.date.accessioned | 2021-06-13T05:55:33Z | - |
| dc.date.available | 2007-07-10 | |
| dc.date.copyright | 2006-07-10 | |
| dc.date.issued | 2006 | |
| dc.date.submitted | 2006-06-30 | |
| dc.identifier.citation | References
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Luh, { A note on commuting automorphisms of rings}, Amer. Math. Monthly 77(1) (1970), 61-62. [Mar]: W.S. Martindale 3rd, { Prime rings satisfying a generalized polynomial identity}, J. Algebra 12 (1969), 576-584. [Mat]: J. Matczuk, { Extended centroids of skew polynomial rings }, Math. J. Okayama Univ. 30 (1988), 13--20. [Ma1]: J.H. Mayne, { Centralizing automorphisms of prime rings}, Canad. Math. Bull., 19 (1976), 113-115. [Ma2]: J.H. Mayne, { Centralizing automorphisms of Lie ideals in prime rings}, Canad. Math. Bull., 35 (1992), 510-514. [PJ]: K.-H. Park and Y.-S. Jung, { Skew-commuting and commuting mappings in rings}, Aequationes Math. 64 (2002), 136-144. [Po]: E.C. Posner, { Derivations in prime rings}, Proc. Amer. Math. Soc. 8 (1957), 1093-1100. [Ro]: L.H. Rowen, { On rings with central polynomials}, J. Algebra 31 (1974), 393-426. [Vi]: O.M. Di Vincenzo, { A result on derivations with algebraic values}, Canad. Math. Bull. 29 (1986), 432-437. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/34136 | - |
| dc.description.abstract | Abstract
This thesis focuses on differential identities and constants of algebraic automorphisms in prime rings. In Chapter 1 we prove that an algebra over a field with a finite dimensional maximal subalgebra must be finite dimensional. In Chapters 2 and 3 we consider certain differential identities in prime rings. Firstly, we show that if a prime algebra admits a nonzero generalized skew derivation with algebraic values of bounded degree, then the algebra must be a primitive ring with nonzero socle and its associated division algebra is a finite-dimensional central division algebra. Secondly, we determine the structure of a prime ring admitting an additive n-commuting map which is linear over its center. In Chapter 4 we consider constants of algebraic automorphisms in prime rings. Let R be a prime ring with extended centroid C. For an automorphism sig of R we let R^(sig)≡{x in R | sig(x)=x}, the subring of constants of sig on R. Suppose that the automorphism sig is algebraic over C. We give a complete characterization of the primeness and semiprimeness of the subring R^(sig). Moreover, if the subring R^(sig) is a prime PI-ring, we obtain the PI-degree of R^(sig) in terms of that of the whole ring R and the inner degree of the automorphism sig. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T05:55:33Z (GMT). No. of bitstreams: 1 ntu-95-F89221001-1.pdf: 333144 bytes, checksum: 0fe1b8bf2c3716bafeb8ae4c18311e17 (MD5) Previous issue date: 2006 | en |
| dc.description.tableofcontents | Contents
Abstract Introduction 1 Chapter 0. Preliminaries 6 Chapter 1. Algebras with a Finite-Dimensional Maximal Subalgebra 12 Chapter 2. Generalized Skew Derivations with Algebraic Values of Bounded Degree 16 Chapter 3. n-Commuting Maps on Prime Rings 25 Chapter 4. Constants of Algebraic Automorphisms 33 References 49 | |
| dc.language.iso | en | |
| dc.subject | 自同構 | zh_TW |
| dc.subject | 導算等式 | zh_TW |
| dc.subject | 導算 | zh_TW |
| dc.subject | derivation | en |
| dc.subject | differential identity | en |
| dc.subject | prime | en |
| dc.subject | automorphism | en |
| dc.title | 質環上之導算等式與代數自同構之常值 | zh_TW |
| dc.title | Differential Identities and Constants of Algebraic Automorphisms in Prime Rings | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 94-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 李白飛,莊正良,林哲雄,王彩蓮 | |
| dc.subject.keyword | 導算,導算等式,自同構, | zh_TW |
| dc.subject.keyword | derivation,automorphism,prime,differential identity, | en |
| dc.relation.page | 52 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2006-06-30 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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