Some Identities Involving Generalized Left (T,F)-Derivations in Semiprime Rings
Author Affiliations
- 1Shyamsundarpur High School, P. O.- Hanschara, Dist: Purba Medinipur, 721625, INDIA
Res. J. Mathematical & Statistical Sci., Volume 3, Issue (5), Pages 5-10, May,12 (2015)
Abstract
Let us suppose that R be a semiprime ring with two epimorphisms ?, f and I a nonzero ideal of R. By generalized left (?,f)derivation of R we mean an additive mapping F : R ? R such that F(ab) = ?(a)F(b) + f(b)d(a) holds for all a, b ? R, where d : R ? R is a left(?,f)derivation of R. The goal of the present paper is to study the following identities: (i) F([a, b])= ?([a, b]), (ii) F(a?b)= ?(a?b), (iii) F([a, b])= ?(a?b), (iv) F(a?b) = ?([a, b]), (v) F(ab)±?(ab)?Z(R), (vi) F(ab) ± ?(ba) ? Z(R), for all a, b ? I. Mathematics Subject Classification 2010. 16W25,16W80, 16N60.
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