Record number :

2530908

Title of article :

On Abelian Rings

Author/Authors :

Agayev, Nazim University of Lefke - Department of Computer Engineering, Cyprus , Harmancı, Abdullah Hacettepe University - Department of Mathematics, TURKEY , Halıcıoglu, Sait Ankara Üniversitesi - Department of Mathematics, Turkey

From page :

465

To page :

474

Abstract :

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

Keywords :

α , reduced rings , α , symmetric rings , α , semicommutative rings , α , Armendariz rings , α , abelian rings.

Journal title :

Turkish Journal of Mathematics

Link To Document :