Abstract
In this paper we extend our ideas from reverse derivation towards the Generalized reverse derivations on semiprime rings. In this Paper, we prove that if d is a non-zero reverse derivation of a semi prime ring R and f is a generalized reverse derivation, thenis a strong commutativity preserving. Using this, we prove that R is commutative.
Highlights
Bell and Martindale [3] studied centralizing mappings of semiprime rings and proved that if d is a non-zero derivation of a prime ring R such that [d(x),x] 0, for all x in a nonzero left ideal of R, R is commutative
Bell and Daif [2] investigated commutativity in prime and semiprime rings admitting a derivation or an endomorphism which is strong commutativity preserving on a non-zero right ideal
Bresar and Vukman [5] have studied the notion of reverse derivation and some properties of reverse derivations
Summary
Bell and Martindale [3] studied centralizing mappings of semiprime rings and proved that if d is a non-zero derivation of a prime ring R such that [d(x),x] 0, for all x in a nonzero left ideal of R, R is commutative. Bresar [6] studied centralizing mappings and derivations in prime rings and proved that if U be a non-zero left ideal of a prime ring R and d and g are derivations of R satisfying ( ). Proved that if a prime ring R admits a non-zero reverse derivation, R is commutative. K.Suvarna and D.S.Irfana [10] have studied some properties of prime and semiprime rings with generalized derivations on a non-zero left ideal of R. R, f(x) Z, for all SciPress applies the CC-BY 4.0 license to works we publish: https://creativecommons.org/licenses/by/4.0/
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