Automorphisms and generalized skew derivations which are strong commutativity preserving on polynomials in prime and semiprime rings
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- 作者：Vincenzo De Filippis
- 关键词：generalized skew derivation ; prime ring
- 刊名：Czechoslovak Mathematical Journal
- 出版年：2016
- 出版时间：March 2016
- 年：2016
- 卷：66
- 期：1
- 页码：271-292
- 全文大小：196 KB
- 参考文献：[1] N. Argaç, L. Carini, V. De Filippis: An Engel condition with generalized derivations on Lie ideals. Taiwanese J. Math. 12 (2008), 419–433.MathSciNet MATH
[2] M. Brešar, C. R. Miers: Strong c…ty preserving maps of semiprime rings. Can. Math. Bull. 37 (1994), 457–460.CrossRef MATH
[3] J. -C. Chang: On the identity h(x) = af(x) + g(x)b. Taiwanese J. Math. 7 (2003), 103–113.MathSciNet MATH
[4] C. -L. Chuang: Identities with skew derivations. J. Algebra 224 (2000), 292–335.MathSciNet CrossRef MATH
[5] C. -L. Chuang: Differential identities with automorphisms and antiautomorphisms. II. J. Algebra 160 (1993), 130–171.MathSciNet CrossRef MATH
[6] C. -L. Chuang: Differential identities with automorphisms and antiautomorphisms. I. J. Algebra 149 (1992), 371–404.MathSciNet CrossRef MATH
[7] C. -L. Chuang: GPIs having coefficients in Utumi quotient rings. Proc. Am. Math. Soc. 103 (1988), 723–728.MathSciNet CrossRef MATH
[8] C. -L. Chuang: The additive subgroup generated by a polynomial. Isr. J. Math. 59 (1987), 98–106.MathSciNet CrossRef MATH
[9] C. -L. Chuang, T. -K. Lee: Identities with a single skew derivation. J. Algebra 288 (2005), 59–77.MathSciNet CrossRef MATH
[10] C. -L. Chuang, T. -K. Lee: Rings with annihilator conditions on multilinear polynomials. Chin. J. Math. 24 (1996), 177–185.MathSciNet MATH
[11] V. De Filippis: A product of two generalized derivations on polynomials in prime rings. Collect. Math. 61 (2010), 303–322.MathSciNet CrossRef MATH
[12] O. M. DiVincenzo: On the nth centralizer of a Lie ideal. Boll. Unione Mat. Ital., VII. Ser. 3-A (1989), 77–85.MathSciNet
[13] C. Faith, Y. Utumi: On a new proof of Litoff’s theorem. Acta Math. Acad. Sci. Hung. 14 (1963), 369–371.MathSciNet CrossRef MATH
[14] I. N. Herstein: Topics in Ring Theory. Chicago Lectures in Mathematics, The University of Chicago Press, Chicago, 1969.
[15] N. Jacobson: PI-Algebras: An Introduction. Lecture Notes in Mathematics 441, Sprin- ger, Berlin, 1975.MATH
[16] N. Jacobson: Structure of Rings. American Mathematical Society Colloquium Publica- tions 37, AMS, Providence, 1956.MATH
[17] C. Lanski, S. Montgomery: Lie structure of prime rings of characteristic 2. Pac. J. Math. 42 (1972), 117–136.MathSciNet CrossRef MATH
[18] J. -S. Lin, C. -K. Liu: Strong c…ty preserving maps on Lie ideals. Linear Alge- bra Appl. 428 (2008), 1601–1609.CrossRef MATH
[19] C. -K. Liu: Strong c…ty preserving generalized derivations on right ideals. Monatsh. Math. 166 (2012), 453–465.MathSciNet CrossRef
[20] C. -K. Liu, P. -K. Liau: Strong c…ty preserving generalized derivations on Lie ideals. Linear Multilinear Algebra 59 (2011), 905–915.MathSciNet CrossRef MATH
[21] J. Ma, X. W. Xu, F. W. Niu: Strong c…ty-preserving generalized derivations on semiprime rings. Acta Math. Sin., Engl. Ser. 24 (2008), 1835–1842.MathSciNet CrossRef MATH
[22] W. S. Martindale III: Prime rings satisfying a generalized polynomial identity. J. Algebra 12 (1969), 576–584.MathSciNet CrossRef MATH
[23] E. C. Posner: Derivations in prime rings. Proc. Am. Math. Soc. 8 (1958), 1093–1100.MathSciNet CrossRef MATH
[24] T. -L. Wong: Derivations with power-central values on multilinear polynomials. Algebra Colloq. 3 (1996), 369–378.MathSciNet MATH - 作者单位：Vincenzo De Filippis (1)
1. MIFT at University of Messina, Viale Stagno d’Alcontres 31, I-98166, Messina, Italy - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics
Analysis
Convex and Discrete Geometry
Ordinary Differential Equations
Mathematical Modeling and IndustrialMathematics - 出版者：Springer Netherlands
- ISSN：1572-9141
文摘
Let R be a prime ring of characteristic different from 2, Q r its right Martindale quotient ring and C its extended centroid. Suppose that F, G are generalized skew derivations of R with the same associated automorphism α, and p(x 1, …, x n ) is a non-central polynomial over C such that $$\left[ {F(x),\alpha (y)} \right] = G(\left[ {x,y} \right])$$ for all x, y ∈ {p(r 1, …, r n ): r 1, …, r n ∈ R}. Then there exists λ ∈ C such that F(x) = G(x) = λα(x) for all x ∈ R. Keywords generalized skew derivation prime ring MSC 2010 16W25 16N60 Page %P Close Plain text Look Inside Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions Register for Journal Updates About This Journal Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Related Content Supplementary Material (0) References (24) References[1] N. Argaç, L. Carini, V. De Filippis: An Engel condition with generalized derivations on Lie ideals. Taiwanese J. Math. 12 (2008), 419–433.MathSciNetMATH[2] M. Brešar, C. R. Miers: Strong c…ty preserving maps of semiprime rings. Can. Math. Bull. 37 (1994), 457–460.CrossRefMATH[3] J. -C. Chang: On the identity h(x) = af(x) + g(x)b. Taiwanese J. Math. 7 (2003), 103–113.MathSciNetMATH[4] C. -L. Chuang: Identities with skew derivations. J. Algebra 224 (2000), 292–335.MathSciNetCrossRefMATH[5] C. -L. Chuang: Differential identities with automorphisms and antiautomorphisms. II. J. Algebra 160 (1993), 130–171.MathSciNetCrossRefMATH[6] C. -L. Chuang: Differential identities with automorphisms and antiautomorphisms. I. J. Algebra 149 (1992), 371–404.MathSciNetCrossRefMATH[7] C. -L. Chuang: GPIs having coefficients in Utumi quotient rings. Proc. Am. Math. Soc. 103 (1988), 723–728.MathSciNetCrossRefMATH[8] C. -L. Chuang: The additive subgroup generated by a polynomial. Isr. J. Math. 59 (1987), 98–106.MathSciNetCrossRefMATH[9] C. -L. Chuang, T. -K. Lee: Identities with a single skew derivation. J. Algebra 288 (2005), 59–77.MathSciNetCrossRefMATH[10] C. -L. Chuang, T. -K. Lee: Rings with annihilator conditions on multilinear polynomials. Chin. J. Math. 24 (1996), 177–185.MathSciNetMATH[11] V. De Filippis: A product of two generalized derivations on polynomials in prime rings. Collect. Math. 61 (2010), 303–322.MathSciNetCrossRefMATH[12] O. M. DiVincenzo: On the nth centralizer of a Lie ideal. Boll. Unione Mat. Ital., VII. Ser. 3-A (1989), 77–85.MathSciNet[13] C. Faith, Y. Utumi: On a new proof of Litoff’s theorem. Acta Math. Acad. Sci. Hung. 14 (1963), 369–371.MathSciNetCrossRefMATH[14] I. N. Herstein: Topics in Ring Theory. Chicago Lectures in Mathematics, The University of Chicago Press, Chicago, 1969.[15] N. Jacobson: PI-Algebras: An Introduction. Lecture Notes in Mathematics 441, Sprin- ger, Berlin, 1975.MATH[16] N. Jacobson: Structure of Rings. American Mathematical Society Colloquium Publica- tions 37, AMS, Providence, 1956.MATH[17] C. Lanski, S. Montgomery: Lie structure of prime rings of characteristic 2. Pac. J. Math. 42 (1972), 117–136.MathSciNetCrossRefMATH[18] J. -S. Lin, C. -K. Liu: Strong c…ty preserving maps on Lie ideals. Linear Alge- bra Appl. 428 (2008), 1601–1609.CrossRefMATH[19] C. -K. Liu: Strong c…ty preserving generalized derivations on right ideals. Monatsh. Math. 166 (2012), 453–465.MathSciNetCrossRef[20] C. -K. Liu, P. -K. Liau: Strong c…ty preserving generalized derivations on Lie ideals. Linear Multilinear Algebra 59 (2011), 905–915.MathSciNetCrossRefMATH[21] J. Ma, X. W. Xu, F. W. Niu: Strong c…ty-preserving generalized derivations on semiprime rings. Acta Math. Sin., Engl. Ser. 24 (2008), 1835–1842.MathSciNetCrossRefMATH[22] W. S. Martindale III: Prime rings satisfying a generalized polynomial identity. J. Algebra 12 (1969), 576–584.MathSciNetCrossRefMATH[23] E. C. Posner: Derivations in prime rings. Proc. Am. Math. Soc. 8 (1958), 1093–1100.MathSciNetCrossRefMATH[24] T. -L. Wong: Derivations with power-central values on multilinear polynomials. Algebra Colloq. 3 (1996), 369–378.MathSciNetMATH About this Article Title Automorphisms and generalized skew derivations which are strong commutativity preserving on polynomials in prime and semiprime rings Journal Czechoslovak Mathematical Journal Volume 66, Issue 1 , pp 271-292 Cover Date2016-03 DOI 10.1007/s10587-016-0255-0 Print ISSN 0011-4642 Online ISSN 1572-9141 Publisher Springer Berlin Heidelberg Additional Links Register for Journal Updates Editorial Board About This Journal Manuscript Submission Topics Mathematics, general Analysis Convex and Discrete Geometry Ordinary Differential Equations Mathematical Modeling and Industrial Mathematics Keywords generalized skew derivation prime ring 16W25 16N60 Industry Sectors Biotechnology Pharma Authors Vincenzo De Filippis (1) Author Affiliations 1. 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