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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/38894完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 李秋坤(Tsiu-Kwen Lee) | |
| dc.contributor.author | Hung-Yung Chen | en |
| dc.contributor.author | 陳弘遠 | zh_TW |
| dc.date.accessioned | 2021-06-13T16:51:10Z | - |
| dc.date.available | 2010-03-03 | |
| dc.date.copyright | 2010-03-03 | |
| dc.date.issued | 2005 | |
| dc.date.submitted | 2005-06-22 | |
| dc.identifier.citation | References
[1] K.I. Beidar and M. Bresar, Extended Jacobson Density Theorem for Rings with Derivations and Automorphisms, Israel J. Math., 122 (2001), 317-346. [2] K.I. Beidar, W.S. Martindale 3rd and A.V. Mikhalev, \Rings with Generalized Identities', Monographs and Textbooks in Pure and Applied Mathematics, 196. Marcel Dekker, Inc., New York, 1996. [3] L. Carini and V.De Filippis, Commutators with power central values on a Lie ideal, Paci c J. Math., 193(2) (2000), 269-278. [4] C.-L. Chuang, GPIs having coe cients in Utumi quotient rings, Proc. Amer. Math. Soc., 103 (1988), 723-728. [5] C.-L. Chuang, Di erential identities with automorphisms and antiautomor- phisms, I, J. Algebra 149 (1992), 371{404. [6] C.-L. Chuang, Di erential identities with Automorphisms and Antiautomor- phisms II, J. Algebra, 160 (1993), 130-171. [7] C.-L. Chuang and T.-K. Lee, Identities with a single skew derivation, J.Algebra (2005), to appear. [8] I.N. Herstein, Center-like elements in prim rings, J.Algebra, 60 (1979), 567-574. [9] A. Giambruno and I. N. Herstein, Derivations with nilpotent values, Rend. Circ. Mat. Palermo 30 (1981), 199{206. [10] N. Jacobson, 'Structure of Rings', Amer. Math. Soc. Colloquim Publ., Prov- idence, 1956. [11] V.K. Kharchenko, Generalized identities with automorphisms, Algebra i Logika, 14(2) (1975), 215-237. (English Translation, Algebra and Logic, 14(2) (1975), 132-148.) [12] V.K. Kharchenko, Di erential identities of prime rings, Algebra i Logika, 17 (1978), 220-238. (English Translation, Algebra and Logic, 17 (1978), 154-168.) [13] C. Lanski, An Engel condition with derivation, Proc. Amer. Math. Soc., 118(3) (1993), 731-734. [14] C. Lanski, Di erential identities, Lie ideals and Posner's theorems, Paci c J. Math., 134(2) (1998), 275-297. [15] C. Lanski and S. Montgomery, Lie struture of prime rings of characteristic 2, Paci c J. Math., 42 (1972), 117-136. [16] T.-K. Lee, Generalized derivations of left faithful rings, Comm. Algebra, 27(8) (1999), 4057-4073. [17] T.-K. Lee, Semiprime rings with di erential identities, Bull. Inst. Math. Acad. Sinica, 20 (1992), 27-38. [18] W.S. Martindale, III, Prime rings satisfying a generalized polynomial identity, J. Algebra, 12 (1969), 576-584. [19] E.C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093-1100. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/38894 | - |
| dc.description.abstract | In the thesis we study the problem concerning skew derivations with
power central-values on commutators in prime rings. Precisely, we prove the following two main results. Main Theorem 1. Let R be a prime ring with charR 6= 2, an automorphism of R, and d a -derivation of R. If [d([x; y]); [x; y]]n = 0 for all x; y 2 R, then either d = 0 or R is a commutative ring. Main Theorem 2. Let R be a prime ring, with an automorphism , and d a nonzero -derivation of R. Suppose that [d(x); x]n 2 Z(R) for all x 2 R. If either charR = 0 or charR > n, then dimC RC 4. As a corollary to Main Theorem 1, we have the following result. Corollary. Let R be a prime ring with charR 6= 2, an automorphism of R, L a noncentral Lie ideal of R, and d a -derivation of R. If [d(x); x]n = 0 for all x 2 L, then either d = 0 or R is a commutative ring. 2000 Mathematics Subject Classi cation. 16R53, 16R60, 16N60. Key words and phrases. Automorphism, prime ring, Martindale quotient ring, skew derivation, M-inner. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T16:51:10Z (GMT). No. of bitstreams: 1 ntu-94-R91221001-1.pdf: 173962 bytes, checksum: 655dba5c1e76901e608ce40a6ab42b66 (MD5) Previous issue date: 2005 | en |
| dc.description.tableofcontents | Contents
1.Introduction 1 2. Preliminaries 4 3. Results on Matrix Rings 7 4. Proofs of Main Theorems 15 5. Counterexamples with char R=2 29 References 30 | |
| dc.language.iso | en | |
| dc.subject | M-內部型 | zh_TW |
| dc.subject | 同構 | zh_TW |
| dc.subject | 質環 | zh_TW |
| dc.subject | 馬汀達爾除環 | zh_TW |
| dc.subject | 斜導算 | zh_TW |
| dc.subject | prime ring | en |
| dc.subject | M-inner | en |
| dc.subject | skew derivation | en |
| dc.subject | Martindale quotient ring | en |
| dc.subject | Automorphism | en |
| dc.title | Skew Derivations With Power Central-Values On Commutators | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 93-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 李白飛,王彩蓮 | |
| dc.subject.keyword | 同構,質環,馬汀達爾除環,斜導算,M-內部型, | zh_TW |
| dc.subject.keyword | Automorphism,prime ring,Martindale quotient ring,skew derivation,M-inner, | en |
| dc.relation.page | 31 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2005-06-23 | |
| 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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