Sait HALICIOĞLU, Abdullah HARMANCI, Nazim AGAYEV

8698

On Abelian Rings

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

Anahtar Kelimeler:

a-reduced rings, a-symmetric rings, a-semicommutative rings, a-Armendariz rings, a-abelian rings

On Abelian Rings

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

Keywords:

a-reduced rings, a-symmetric rings, a-semicommutative rings, a-Armendariz rings, a-abelian rings,

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

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