On Abelian Rings


Agayev N., Harmanci A., HALICIOĞLU S.

TURKISH JOURNAL OF MATHEMATICS, vol.34, no.4, pp.465-474, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 4
  • Publication Date: 2010
  • Doi Number: 10.3906/mat-0711-1
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.465-474

Abstract

Let alpha be an endomorphism of an arbitrary ring R with identity In this note, we introduce the notion of alpha-abelian rings which generalizes abelian rings We prove that alpha-reduced rings, alpha-symmetric rings, alpha-semicommutative rings and alpha-Armendariz rings are alpha-abelian For a right principally projective ring R, we also prove that R is alpha-reduced if and only if R is alpha-symmetric if and only if R is alpha-semicommutative if and only if R is alpha-Armendariz if and only if R is alpha-Armendariz of power series type if and only if R is alpha-abelian