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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/34711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 | Yen-Jen Chen | en |
| dc.contributor.author | 陳彥任 | zh_TW |
| dc.date.accessioned | 2021-06-13T06:24:07Z | - |
| dc.date.available | 2006-01-27 | |
| dc.date.copyright | 2006-01-27 | |
| dc.date.issued | 2006 | |
| dc.date.submitted | 2006-01-23 | |
| dc.identifier.citation | [BMM] K. I. Beidar, W. S. Martindale 3rd and A. V. Mikhalev, “Rings with Gener-alized Identities”, Marcel Dekker, Inc., New York-Basel-Hong Kong, 1996.
[Br1] M. Breˇsar, Centralizing mappings and derivations in prime rings, J. Algebra 156 (1993), 385–394. [Br2] M. Breˇsar, Commuting traces of biadditive mappings, commutativity–preserving mappings and Lie mappings, Trans. Amer. Math. Soc. 355 (1993), 525–546. [Br3] M. Breˇsar, On Generalized biderivations and related maps, J. Algebra 172 (1995), 746–786. [Ch] C.-L. Chuang, GPIs having coefficients in Utumi quotient rings, Proc. Amer.Math. Soc. 103 (1988), 723–728. [CL1] C.-L. Chuang and T.-K. Lee, Algebraic derivations with constants satisfying a polynomial identity, Israel J. Math. 138 (2003), 43–60. [CL2] C.-L. Chuang and T.-K. Lee, Nilpotent derivations, J. Algebra 287(2) (2005),381–401. [FU] C. Faith and Y. Utumi, On a new proof of Litoff’s theorem, Acta Math. Acad.Sci. Hung. 14 (1963), 369–371. [Gr] P. Grzeszczuk, Constants of algebraic derivations, Comm. Algebra 21(6) (1993),1857–1868. [Hv] B. Hvala, Generalized derivations in rings, Comm. Algebra 26(4) (1998), 1147–1166. [Ja] N. Jacobson, “PI-Algebras: an Introduction”, Lecture Notes in Math. 441,Springer–Verlag, Berlin and New York, 1975. [Kh1] V. K. Kharchenko, Differential identities of prime rings, Algebra i Logika 17(1978), 220–238 (Engl. Transl., Algebra and Logic 17 (1978), 154–168). [Kh2] V. K. Kharchenko, Differential identities of semiprime rings, Algebra i Logika 18 (1979), 86–119 (Engl. Transl., Algebra and Logic 18 (1979), 58–80). [La] C. Lanski, Differential identities of prime rings, Kharchenko’s theorem, and ap-plications, Contemporary Mathematics 124 (1992), 111-128. [Le1] T.-K. Lee, Semiprime rings with differential identities, Bull. Inst. Math. Acad.Sinica 20 (1992), 27–38. [Le2] T.-K. Lee, Derivations with Engel conditions on polynomials, Algebra Collo-quium 5 (1998), 13–24. [Le3] T.-K. Lee, Generalized derivations of left faithful rings, Comm. Algebra 27(8)(1999), 4057–4073. [LL] T.-K. Lee and T.-C. Lee, Commuting additive mappings in semiprime rings,Bull. Inst. Math. Acad. Sinica 24 (1996), 259–268. [LM] C. Lanski and S. Montgomery, Lie structure of prime rings of characteristic 2,Pacific Journal of Mathematics 42 (1972), 117-136. [LS] T.-K. Lee and W.-K. Shiue, Derivations cocentralizing polynomials, Taiwanese J. Math. 2 (1998), 457–467. [Ma1] W. S. Martindale, 3rd, Prime rings satisfying a generalized polynomial identity,J. Algebra 12 (1969), 576-584. [Ma2] W. S. Martindale, 3rd, On semiprime P.I. rings, Proc. Amer. Math. Soc. 40(1973), 365–369. [Po] E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957),1093–1100. [Ro] L. H. Rowen, Maximal quotients of semiprime PI-algebras, Trans. Amer. Math.Soc. 196 (1974), 127–135. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/34711 | - |
| dc.description.abstract | We show two results in this thesis. Firstly, let R be a semiprime ring with extended centroid C and with Martindale left ring of quotients R_F. Suppose that δ : R → R is a left R_F-integral derivation. Let R(δ) (resp. R_F(δ)) denote the subring of constants of δ on R (resp. R_F). We prove: (I) If the R_F-integral degree of δ is m, then δ is C-integral of degree less than or equal to m^2. (II) R(δ) and R_F(δ) satisfy the same PIs.
Secondly, let R be a prime ring with extended centroid C and let f(X_1, . . . ,X_t) be a polynomial over C, which is not central-valued on RC. Let g be a generalized derivation of R, which is not of the form x : R → λx for some λ in C. Suppose that [g(f(x_1, . . . , x_t)), f(x_1, . . . , x_t)] in C for all x_i in R. Then one of the following two cases holds except when charR = 2 and dim_C RC = 4: (1) g(x) = λx + d(x) for some λ in C, where d is an X-outer derivation of R, charR = 2 and f(X_1, . . . ,X_t)2 is central-valued on RC. (2) g(x) = ax + x(a + β) for some a in R_F and some β in C, and f(X_1, . . . ,X_t)2 is central-valued on RC. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T06:24:07Z (GMT). No. of bitstreams: 1 ntu-95-R92221023-1.pdf: 247021 bytes, checksum: 3ca2fb59e96dbf68b6186311d5974e6c (MD5) Previous issue date: 2006 | en |
| dc.description.tableofcontents | Table of Contents iv
Acknowledgements v Abstract vi 1 PIs and Constants of Algebraic Derivations 1 2 Posner’s Theorem for Generalized Derivations 11 Bibliography 21 | |
| dc.language.iso | en | |
| dc.subject | 多項式等式 | zh_TW |
| dc.subject | Martindale除環 | zh_TW |
| dc.subject | 導算 | zh_TW |
| dc.subject | 一般化導算 | zh_TW |
| dc.subject | 常值 | zh_TW |
| dc.subject | constants | en |
| dc.subject | derivation | en |
| dc.subject | Martindale quotient ring | en |
| dc.subject | generalized derivation | en |
| dc.subject | polynomial identity(PI) | en |
| dc.title | 導算之常值與導算恆等式 | zh_TW |
| dc.title | Constants of Derivations and Differential Identities | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 94-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 李白飛(Pjek-Hwee Lee),王彩蓮(Tsai-Lien Wong) | |
| dc.subject.keyword | Martindale除環,導算,一般化導算,常值,多項式等式, | zh_TW |
| dc.subject.keyword | Martindale quotient ring,derivation,generalized derivation,constants,polynomial identity(PI), | en |
| dc.relation.page | 23 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2006-01-24 | |
| 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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