Open AccessGeneralized (; )-derivations and Left Ideals in Prime and Semiprime Rings
Author(s) -
Abdul Karim Ali,
Hamidur Rahaman
Publication year - 2017
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v13i2.6024
Subject(s) - mathematics , semiprime ring , semiprime , automorphism , prime (order theory) , ideal (ethics) , associative property , pure mathematics , associated prime , ring (chemistry) , prime ring , combinatorics , philosophy , chemistry , organic chemistry , epistemology
Let R be an associative ring, ; be the automorphisms of R, be a nonzero left ideal of R, F : R ! R be a generalized (; )-derivation and d : R ! Rbe an (; )-derivation. In the present paper we discuss the following situations: (i) F(xoy) = a(xy yx), (ii) F([x; y]) = a(xy yx), (iii) d(x)od(y) = a(xy yx) forall x; y 2 and a 2 f0; 1;ô€€€1g. Also some related results have been obtained.