Turkish Journal of Mathematics
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.
DOI
10.3906/mat-0711-1
Keywords
\alpha-reduced rings, \alpha-symmetric rings, \alpha-semicommutative rings, \alpha-Armendariz rings, \alpha-abelian rings
First Page
465
Last Page
474
Recommended Citation
AGAYEV, N, HARMANCI, A, & HALICIOĞLU, S (2010). On Abelian Rings. Turkish Journal of Mathematics 34 (4): 465-474. https://doi.org/10.3906/mat-0711-1
