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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
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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
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