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2024 | OriginalPaper | Chapter

A Commutativity Condition for Semiprime Rings with Generalized Skew Derivations

Author : Francesco Rania

Published in: Advances in Ring Theory and Applications

Publisher: Springer Nature Switzerland

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Abstract

Let R be a semiprime ring of characteristic different from 2, Z(R) its center, Q its right Martindale quotient ring, C its extended centroid, F a generalized skew derivation of R and \(n\ge 1\) a fixed integer such that \(\bigr (F(x)y+F(y)x-[x,y]\bigl )^n=0\), for all \(x,y \in R\). Then R is commutative and \(F=0\).

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previous chapter Non-linear Mappings Preserving Product on Factor von Neumann Algebras

next chapter Results on Generalized Derivations in Prime Rings with Involution

Beidar, K.I.: Rings with generalized identities III. Moscow Univ. Math. Bull. 33, 53–58 (1978)

Beidar, K.I., Martindale, W.S., III., Mikhalev, A.V.: Rings with Generalized Identities. Pure and Applied Math, Dekker, New York (1996)

Chang, J.-C.: On the identitity \(h(x)=af(x)+g(x)b\). Taiwanese J. Math. 7, 103–113 (2003)MathSciNetCrossRef

Cheng, H.-W., Wei, F.: Generalized skew derivations of rings. Adv. Math. 35(2), 237–243 (2006)MathSciNet

Chuang, C.-L.: GPIs having coefficients in Utumi quotient rings. Proc. Amer. Mat. Soc. 103(3), 723–728 (1988)MathSciNetCrossRef

Chuang, C.-L.: Differential identities with automorphisms and antiautomorphisms I. J. Algebra 149, 371–404 (1992). https://doi.org/10.1016/0021-8693(92)90023-F

Chuang, C.-L.: Differential identities with automorphisms and antiautomorphisms II. J. Algebra 160, 130–171 (1993). https://doi.org/10.1006/jabr.1993.1181

Chuang, C.-L., Lee, T.-K.: Identities with a single skew derivation. J. Algebra 288, 59–77 (2005). https://doi.org/10.1016/j.jalgebra.2003.12.032

De Filippis, V.: A product of two generalized derivations on polynomials in prime rings. Collect. Math. 61, 303–322 (2010). https://doi.org/10.1007/BF03191235

10.

De Filippis, V., Scudo, G.: Strong commutativity and Engel condition preserving maps in prime and semiprime rings. Linear Multilinear Algebra 61/7, 917–938 (2013). https://doi.org/10.1080/03081087.2012.716433

11.

De Filippis, V., Rehman, N., Scudo, G.: Certain functional identities involving a pair of generalized skew derivations with nilpotent values on Lie ideals. Commun. Algebra 51(2), 711–723 (2023). https://doi.org/10.1080/00927872.2022.2110888

12.

Erickson, T.S., Martindale, W.S., III., Osborn, J.: Prime nonassociative algebras. Pacific J. Math. 60, 49–63 (1975)

13.

Jacobson, N.: Structure of rings. Amer. Math. Soc, Providence, RI (1964)

14.

Martindale III, W.S.: Prime rings satisfying a generalized polynomial identity. J. Algebra 12, 576–584 (1969). https://doi.org/10.1016/0021-8693(69)90029-5

15.

Rania, F., Scudo, G.: Power values of generalized skew derivations preserving Jordan product on Lie ideals. Commun. Algebra 5(06), 2336–2348 (2022). https://doi.org/10.1080/00927872.2021.2006208

16.

Sandhu, G.S.: On Herstein’s identity in prime rings. Algebra Discrete Math. 33(1), 145–155 (2022). http://dx.doi.org/10.12958/adm1581

Title: A Commutativity Condition for Semiprime Rings with Generalized Skew Derivations
Author: Francesco Rania
Publisher: Springer Nature Switzerland
Book: Advances in Ring Theory and Applications
Print ISBN: 978-3-031-50794-6

Electronic ISBN: 978-3-031-50795-3

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-50795-3_25

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