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http://dx.doi.org/10.14317/jami.2022.915

COMMUTATIVITY OF PRIME GAMMA NEAR RINGS WITH GENERALIZED DERIVATIONS  

MARKOS, ADNEW (Department of Mathematics, College of Natural Sciences, Jimma University)
MIYAN, PHOOL (Department of Mathematics, College of Natural and Computational Sciences, Haramaya University)
ALEMAYEHU, GETINET (Department of Mathematics, College of Natural and Computational Sciences, Haramaya University)
Publication Information
Journal of applied mathematics & informatics / v.40, no.5_6, 2022 , pp. 915-923 More about this Journal
Abstract
The purpose of the present paper is to obtain commutativity of prime Γ-near-ring N with generalized derivations F and G with associated derivations d and h respectively satisfying one of the following conditions:(i) G([x, y]α = ±f(y)α(xoy)βγg(y), (ii) F(x)βG(y) = G(y)βF(x), for all x, y ∈ N, β ∈ Γ (iii) F(u)βG(v) = G(v)βF(u), for all u ∈ U, v ∈ V, β ∈ Γ,(iv) if 0 ≠ F(a) ∈ Z(N) for some a ∈ V such that F(x)αG(y) = G(y)αF(x) for all x ∈ V and y ∈ U, α ∈ Γ.
Keywords
Prime gamma near ring; generalized derivation; semigroup ideal; commutativity;
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Times Cited By KSCI : 2  (Citation Analysis)
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