ON DIVERSITY OF GENERALIZED REVERSE DERIVATIONS IN RINGS

Authors:

Yaqoub Ahmed,M. Aslam,

DOI NO:

https://doi.org/10.26782/jmcms.2020.06.00010

Keywords:

Reverse derivations,Prime rings,Semiprime rings,Involution,

Abstract

In this article, we study the diversity in generalized reverse derivation by defining L*, R* and ( , )-*- Generalized reverse derivation in rings. We introduce some conditions which make these generalized reverse derivations and their associated *-reverse derivations to be commuting. Moreover, we discuss the conditions on these mappings that enforce the rings to be commutative

Refference:

I. A. Aboubakr and S. Gonzalez, Generalized reverse derivations on semiprime rings, Siberian Math. J. 56(2) (2015), 199–205.

II. Filippov V. T., On δ-derivations of Lie algebras, Siberian Math. J., 39, No. 6, 1218–1230 (1998).

III. Filippov V. T., δ-Derivations of prime Lie algebras, Siberian Math. J., 40, No. 1, 174–184 (1999).

IV. Filippov V. T., On δ-derivations of prime alternative and Malcev algebras, Algebra and Logic 39 (2000), 354–358.

V. Gölbasi¨O. and Kaya K., “On Lie ideals with generalized derivations,” Siberian Math. J., 47, No. 5, 862–866 (2006).

VI. Herstein I. N., Jordan derivations of prime rings,”Proc. Amer. Math. Soc., 8, No. 6, 1104–1110 (1957).

VII. Herstein I. N., A Note on Derivations II, Canad. Math. Bull. 22 (4), (1979), 509-511.

VIII. Hopkins N. C., Generalized derivations of nonassociative algebras, Nova J. Math. Game Theory Algebra, 5, No. 3, 215–224 (1996).

IX. Kaygorodov I. B., On δ-derivations of classical Lie superalgebras, Siberian Math. J., 50, No. 3, 434–449 (2009).

X. Kaygorodov I. B., δ-Superderivations of simple finite-dimensional Jordan and Lie superalgebras, Algebra and Logic, 49, No. 2, 130–144 (2010).

XI. Kaygorodov I. B., On (n + 1)-ary derivations of simple n-aryMalcev algebras, St. Petersburg Math. J., 25, No. 4,575–585 (2014).

XII. M. Ashraf, A. Ali, S. Ali, Some commutatively theorems for rings with generalized derivations, Southeast Asian Bull. Math. 31 (2007), 415–421.

XIII. M. Ashraf, N. Rehman, On derivations and commutatively in prime rings, East-West J. Math. 3 (2001), 87–91.

XIV. M. Breˇsar, On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), 89–93.

XV. M. Breˇsar and J. Vukman, On some additive mappings in rings with involution, A equations Math. 38 (1989), 178–185.

XVI. NA. Dar, On∗-centralizing mappings in rings with involution, Georgian Math. J. 21 (2014), no. 1, 25–28.

XVII. S. Ali, B. Dhara, A. Foˇsner, Some commutatively theorems concerning additive maps and derivations on semiprime rings, in : Contemporary Ring Theory 2011, World Scientific, Hackensack (2012), 135–143.

XVIII. S.K. Tiwari, R.K. Sharma, and B. Dhara, B. Some theorems of commutatively on semiprime rings with mappings, Southeast Asian Bull.Math. 42 (2018), 579–592.

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