請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/22491完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 李秋坤 | zh_TW |
| dc.contributor.author | 莊宗穎 | zh_TW |
| dc.contributor.author | Tzung-Ying Chuang | en |
| dc.date.accessioned | 2021-06-08T04:19:03Z | - |
| dc.date.available | 2024-09-16 | - |
| dc.date.copyright | 2010-07-30 | - |
| dc.date.issued | 2010 | - |
| dc.date.submitted | 2002-01-01 | - |
| dc.identifier.citation | [1] 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.
[2] M. Brešar, On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J. 33(1) (1991), 89–93. [3] M. Brešar, Characterizing homomorphisms, derivations and multipliers in rings with idempotents, Proc. Roy. Soc. Edinburgh Sect. A 137(1) (2007), 9–21. [4] C.-M. Chang and T.-K. Lee, Derivations and central linear generalized polynomials in prime rings, Southeast Asian Bull. Math. 21(3) (1997), 215–225. [5] C.-L. Chuang, On invariant additive subgroups, Israel J. Math. 57(1) (1987), 116–128. [6] C.-L. Chuang, GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc. 103(3) (1988), 723–728. [7] B. Felzenszwalb, On a result of Levitzki, Canad. Math. Bull. 21(2) (1978), 241– 242. [8] I.N. Herstein, “Noncommutative rings”, The Carus Mathematical Monographs, No.15 Published by The Mathematical Association of America 1968. [9] I.N. Herstein, “Topics in ring theory”, The University of Chicago Press, Chicago, Ill.-London 1969. [10] I.N. Herstein,Center-like elements in prime rings, J. Algebra 12(2) (1979), 567–574. [11] N. Jacobson, “PI-algebras: an introduction”, Lecture Notes in Mathematics 441. Springer-Verlag, Berlin, 1975. [12] K.-W. Jun and K.-H. Kim, Derivations on prime rings and banach algebras, Bull. Korean Math. Soc. 38(4) (2001),709–718. [13] V.K. Kharchenko, Differential identities of prime rings, (Russian) Algebra i Logika 17(2) (1978), 220–238, 242–243. [14] T.-K. Lee, Semiprime rings with differential identities, Bull. Inst. Math. Acad. Sinica 20(1) (1992), 27–38. [15] T.-K. Lee, Power reduction property for generalized identities of one-sided ideals, Algebra Colloq. 3(1) (1996), 19–24. [16] T.-K. Lee and W.-K. Shiue, Derivations cocentralizing polynomials, Taiwanese J. Math. 2(4) (1998), 457–467. [17] T.-K. Lee, Differential identities of Lie ideals or large right ideals in prime rings, Comm. Algebra 27(2) (1999), 793–819. [18] T.-K. Lee, Generalized derivations of left faithful rings, Comm. Algebra 27(8) (1999), 4057–4073. [19] T.-K. Lee, Generalized skew derivations characterized by acting on zero products, Pacific J. Math. 216(2) (2004), 293–301. [20] T.-K. Lee and Yiqiang Zhou, An identity with generalized derivations, J. Algebra Appl. 8(3) (2009), 307–317 [21] W.S. Martindale 3rd, Prime rings satisfying a generalized polynomial identity, J. Algebra. 12 (1969), 576–584. [22] A.B. Thaheemand M.S. Samman, A note on α-derivations on semiprime rings, Demonstratio Math. 34(4) (2001), 783–788. [23] J. Vukman, Identities with derivations on rings and Banach algebras, Glas. Mat. Ser. III 40(2) (2005), 189–199. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/22491 | - |
| dc.description.abstract | 令R是一個質環且dimC RC > 4, 令D,G是R的泛導算, 令m, n是固定的正整數.然後D(xm)xn− xnG(xm) ∈C 若且爲若以下兩個條件成立:(1) 存在w 屬於Q, R的Martindale 對稱除環, 使得D(x) = xw且G(x) = wx 對於所有的x屬於R (2)w屬於C或者是xm和xn是C相依的對於所有的x屬於R. 我們也將討論非交換李理想的例. | zh_TW |
| dc.description.abstract | Let R be a prime ring and dimC RC > 4, let D,G be two generalized derivations of R, and let m, n be two fixed positive integers. Then D(xm)xn−xnG(xm) ∈C for all x ∈R iff the following two conditions hold: (1) There exists w 2 Q, the symmetric Martindale quotient ring of R, such that D(x) = xw and G(x) = wx for all x ∈R; (2) either w ∈C, or xm and xn are C-dependent for all x ∈R. We also consider the situation of noncommutative Lie ideals. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T04:19:03Z (GMT). No. of bitstreams: 1 ntu-99-R96221031-1.pdf: 302336 bytes, checksum: 30450ad98d68b44d9ec335e9221579d4 (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | 口試委員審定書…………………………………………………… i
誌謝………………………………………………………………… ii 摘要………………………………………………………………… iii Abstract……………………………………………………………… iv 第一章 Introduction and Results ………………………………… 1 第二章 Proof of Theorem 1.1 ………………………………… 2 第三章 Proof of Theorem 1.2 ………………………………… 7 Reference …………………………………………………………… 12 | - |
| dc.language.iso | zh_TW | - |
| dc.title | 具泛導算之中心恆等式 | zh_TW |
| dc.title | A central identity with generalized derivations | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 98-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 李白飛;王彩蓮 | zh_TW |
| dc.contributor.oralexamcommittee | ;; | en |
| dc.subject.keyword | 質環,(廣)導算,李理想,PI,GPI, | zh_TW |
| dc.subject.keyword | Prime ring,(generalized) derivation,Lie ideal,PI,GPI, | en |
| dc.relation.page | 13 | - |
| dc.identifier.doi | 10.6342/NTU.2010.10583 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2010-07-23 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 數學系 | - |
| 顯示於系所單位： | 數學系 | |
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