Abstract
Abstract
We present the notion of generalized reverse derivation on Γ-semiring in this article and we prove that a prime Γ-semiring with center CΓ stratifying assumption (*) aαbβc = aβbαc, for all a, b, c S and α, Γ and I be a non-zero right ideal of S such that S admits a generalized reverse derivation f associated with a reverse derivation d satisfying d(CΓ) ≠ 0, if S satisfies any one of the properties:
(i) f(aαb) + aαb Γ
(ii) f([a, b]α) + [f(a), b]α Γ
(iii) f([a, b]α) + [f(a), f(b)]α Γ
(iv) [f(a), b]α + [a, f(b)]α Γ
For of the all a, b I and α Γ, then S is commutative.
Subject
General Physics and Astronomy
Reference9 articles.
1. On a generalization of the ring theory;Nobusawa;Osaka. J. Math.,1964
2. Γ –semirings-I;Murali Krishna Rao;Southeast Asian Bull. of Math.,1995
3. Γ –semirings-II;Murali Krishna Rao;Southeast Asian Bull. of Math.,1997
4. On derivations of prime Γ–semirings;Javed;Southeast Asian Bull. Math.,2013