Some results on sigma-ideal of sigma-prime ring


TÜRKMEN S., AYDIN N.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.44, no.5, pp.1147-1156, 2015 (Peer-Reviewed Journal) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 5
  • Publication Date: 2015
  • Doi Number: 10.15672/hjms.2015449665
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1147-1156

Abstract

Let R be a sigma-prime ring with characteristic not 2, Z (R) be the center of R, I be a nonzero sigma-ideal of R, alpha, beta : R -> R be two automorphisms, d be a nonzero (alpha, beta)-derivation of R and h be a nonzero derivation of R : In the present paper, it is shown that (i) If d (I) subset of C-alpha,C-beta and beta commutes with sigma then R is commutative. (ii) Let alpha and beta commute with sigma. If a is an element of I boolean AND S-sigma (R) and [d(I), a](alpha,beta) subset of C-alpha,C-beta then a is an element of Z(R). (iii) Let alpha, beta and h commute with sigma. If dh (I) subset of C-alpha,C- beta and h(I) subset of I then R is commutative.