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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 李秋坤(Tsiu-Kwen LEE) | |
| dc.contributor.author | Hung-Yuan Chen | en |
| dc.contributor.author | 陳弘遠 | zh_TW |
| dc.date.accessioned | 2021-06-15T06:55:29Z | - |
| dc.date.available | 2011-02-20 | |
| dc.date.copyright | 2011-02-20 | |
| dc.date.issued | 2011 | |
| dc.date.submitted | 2011-02-09 | |
| dc.identifier.citation | [BMM] 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. [BG00] J. Bergen and P. Grzeszczuk, Skew derivations whose invariants satisfy a polynomial identity, J. Algebra 228(2) (2000), 710–737. [Br91] M. Brešar, On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J. 33(1) (1991), 89–93. [Br93] M. Brešar, Centralizing mappings and derivations in prime rings, J. Algebra 156(2) (1993), 385–394. [Br04] M. Brešar, Commuting maps: a survey, Taiwanese J. Math. 8(3) (2004), 361–397. [Br05] M. Brešar, The range and kernel inclusion of algebraic derivations and commuting maps, Quart. J. Math. 56(1) (2005), 31–41. [Ch87] C.-L Chuang, The additive subgroup generated by a polynomial, Israel J. Math. 59(1) (1987), 98–106. [Ch88] C.-L. Chuang, GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc. 103 (1988), 723–728. [Ch90] C.-L. Chuang, On ranges of polynomials in finite matrix rings, Proc. Amer. Math. Soc. 110(2) (1990), 293–302. [CL04] C.-L. Chuang and T.-K. Lee, Algebraic q-skew derivation, J. Algebra 282(1) (2004), 1–22. [CL05-1] C.-L. Chuang and T.-K. Lee, Identities with a single skew derivations., J. Algebra 288(1) (2005), 59–77. [CL05-2] C.-L. Chuang and T.-K. Lee, q-Skew derivations and polynomial identities, Manuscripta Math. 116(2) (2005), 229–243. [CL10] C.-L. Chuang and T.-K. Lee, Density of polynomial maps, Canad. Math. Bull. 53 (2010), 223–229. [CLW08] C.-L. Chuang, T.-K. Lee, and T.-L. Wong, The kernel and range inclusions of integral derivations in semiprime rings, J. Algebra 320(7) (2008) 2643–2658. [FU63] C. Faith and Y. Utumi, On a new proof of Litoff’s theorem, Acta Math. Acad. Sci. Hungar. 14 (1963), 369–371. [Fi09] V.D. Filippis, Generalied derivations with Engel condition on multilinear polynomials, Israel J. Math. 171 (2009), 325–348. [He79] I. N. Herstein, Center-like elements in prime rings, J. Algebra 60(2) (1979), 567–574 [Ja75] N. Jacobson, “PI-algebras: an introduction”, Lecture Notes in Mathematics 441. Springer-Verlag, Berlin, 1975. [Kh75] V.K. Kharchenko, Generalized identities with automorphisms, Algebra i Logi-ka 14 (1975), 132–148. (Engl. Transl., Algebra and Logic 14 (1975), 132–148.) [Kh78] V.K. Kharchenko, Differential identities of prime rings, Algebra i Logika 17 (1978), 220–238. (Engl. Transl., Algebra and Logic 17 (1978), 155–168.) [Kh79] V.K. Kharchenko, Differential identities of semiprime rings, Algebra and Logic 18 (1979), 86–119. [La93] C. Lanski, An Engel condition with derivation, Proc. Amer. Math. Soc. 118 (1993), 731-734. [La92] C. Lanski, Differential identities of prime rings, Kharchenko’s theorem, and applications, Contemp. Math. 124 (1992), 111-128. [LM72] C. Lanski and S. Montgomery, Lie structure of prime rings of characteristic 2, Pacific J. Math. 42 (1972), 117–136. [LL96] P.-H. Lee and T.-K. Lee, Derivations with Engel conditions on multilinear polynomials, Proc. Amer. Math. Soc. 124(9) (1996), 2625–2629. [LW95] P.-H. Lee and T.-L. Wong, Derivations cocentralizing Lie ideals, Bull. Inst. Math. Acad. Sinica 23(1) (1995), 1–5 [Le92] T.-K. Lee, Semiprime rings with differential identities, Bull. Inst. Math. Acad. Sinica 20 (1992), 27–38. [Le98] T.-K. Lee, Derivations with Engel conditions on polynomials, Algebra Colloq. 5 (1998), 13–24. [Le99] T.-K. Lee, Generalized derivations of left faithful rings, Comm. Algebra, 27(8) (1999), 4057–4073. [LS98] T.-K. Lee and W.-K. Shiue, Derivations cocentralizing polynomials, Taiwanese J. Math. 2(4) (1998), 457–467. [LW04] T.-K. Lee and T.-L.Wong, Linear generalized polynomials with finiteness conditions, Comm. Algebra 32(12) (2004), 4535–4542. [Le86] A. Leroy, Algebraic S-derivation over prime rings, Ring theory (Antwerp, 1985) Lecture Notes in Math. 1197 (1986), 114-120. [Ma69] W.S. Martindale III, Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576–584. [MM83] W.S. Martindale III and C.R. Miers, On the iterates of derivations of prime rings, Pacific J. Math. 104(1) (1983), 179–190. [Po57] E.C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093–1100. [Ro80] L.H. Rowen, “Polynomial identities in ring theory”, Pure and Applied Mathematics, 84. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York- London, 1980. [Vu90] J. Vukman, Commuting and centralizing mappings in prime rings, Proc. Amer. Math. Soc. 109 (1990), 47–52. [Wo97] T.-L. Wong, Derivations cocentralizing multilinear polynomials, Taiwanese J. Math. 1(1) (1997), 31–37. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/48404 | - |
| dc.description.abstract | This thesis focuses on kernel inclusions of algebraic automorphisms, generalized derivations with Engel conditions and generalized derivations cocentralizing polynomials. In Chapter 1 we consider algebraic automorphisms with kernel inclusions. Let R be a prime ring. For an automorphism σ of R we let R(σ) def. = {x ∈ R | σ(x) = x}. Assume that σ is algebraic. We characterize the automorphism τ of R such that R(σ) ⊆ R(τ).
In Chapters 2,3 and 4 we consider certain identities with generalized derivations. Firstly, we concern generalized derivations cocentralizing polynomials. Let R be a prime ring with extended centroid C and let f(X1, . . . ,Xt) be a polynomial over C with zero constant term. Let D and G be generalized derivations of R. We characterize D,G and f(X1, . . . ,Xt) satisfying D(f(x1, . . . , xt))f(x1, . . . , xt) − f(x1, . . . , xt)G(f(x1, . . . , xt))∈ C for all x1, . . . , xt in R. Secondly, we consider certain Engel conditions on polynomials with generalized derivations. Precisely, we characterize D and f(X1, . . . ,Xt) such that the following Engel identity is satisfied: [D(f(x1, . . . , xt)), f(x1, . . . , xt)]k= 0 for all x1, . . . , xt in R. At the end, we concern a generalization of the previous two situations. Precisely, we characterize D,G and f(X1, . . . ,Xt) satisfying [D(f(x1, . . . , xt))f(x1, . . . , xt)−f(x1, . . . , xt)G(f(x1, . . . , xt)), f(x1, . . . , xt)]k= 0 for all x1, . . . , xt in R. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T06:55:29Z (GMT). No. of bitstreams: 1 ntu-100-D95221003-1.pdf: 421758 bytes, checksum: 07ba77500807f41b3448afa589aaeff3 (MD5) Previous issue date: 2011 | en |
| dc.description.tableofcontents | Introduction 1
Chapter 0. Preliminaries 6 Chapter 1. Kernel Inclusions of Algebraic Automorphisms 10 Chapter 2. Generalized Derivations Cocentralizing Polynomials 19 Chapter 3. Generalized Derivations with Engel Conditions 43 Chapter 4. Generalized Derivations with Engel Conditions II 59 References 88 | |
| dc.language.iso | en | |
| dc.subject | 推廣微分算子 | zh_TW |
| dc.subject | 質環 | zh_TW |
| dc.subject | 推廣恆等式 | zh_TW |
| dc.subject | 微分等式 | zh_TW |
| dc.subject | Engel條件 | zh_TW |
| dc.subject | 恆心包含關係 | zh_TW |
| dc.subject | 自同構 | zh_TW |
| dc.subject | 協同中心化 | zh_TW |
| dc.subject | Engel Condition | en |
| dc.subject | automorphism | en |
| dc.subject | Prime ring | en |
| dc.subject | GPI | en |
| dc.subject | Differential identity | en |
| dc.subject | kernel inclusion | en |
| dc.subject | generalized derivation | en |
| dc.subject | cocentralizing | en |
| dc.title | 具Engel條件之導算恆等式 | zh_TW |
| dc.title | Differential Identities with Engel Conditions | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 99-1 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 李白飛(Pjek-Hwee Lee),莊正良(Chen-Lian Chuang),王彩蓮(Tsai-Lien Wong),劉承楷(Cheng-Kai Liu) | |
| dc.subject.keyword | 質環,推廣恆等式,微分等式,Engel條件,恆心包含關係,自同構,協同中心化,推廣微分算子, | zh_TW |
| dc.subject.keyword | Prime ring,GPI,Differential identity,Engel Condition,kernel inclusion,automorphism,cocentralizing,generalized derivation, | en |
| dc.relation.page | 90 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2011-02-10 | |
| 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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