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International Journal of Modern Computation, Information and Communication Technology

ISSN 2581-5954

December 2018, Vol. 1, Issue 7, p. 121-125.​​

Characterizations of Derivations on Prime Rings
Kaunda C. Matoke, Donald Odongo, N. B. Okelo*
School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P. O. Box 210-40601, Bondo-Kenya.
*Corresponding author’s e-mail:
bnyaare@yahoo.com

Abstract

In the present paper, we have studied a (α,α)-symmetric derivations D on semiprime rings and prime rings R, we give some results when R admits a (α,α)-symmetric derivations D to satisfy some conditions on R.(i)D([x,y]n+1) =0 for all x, y∈ R. (ii) [D(xn+1),α(y)] = 0 for all x, y ∈R. (iii) [[D(x),α(x)],α(x)]= 0 for all x ∈R. Where α: R →R is an automorphism mapping.

Keywords: Semiprime Ring; Prime Ring; (α,α)-Derivations; (α,α)-Symmetric Derivation.

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