Displaying similar documents to “On a theorem of McCoy”

Rings with divisibility on descending chains of ideals

Oussama Aymane Es Safi, Najib Mahdou, Ünsal Tekir (2024)

Czechoslovak Mathematical Journal

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This paper deals with the rings which satisfy D C C d condition. This notion has been introduced recently by R. Dastanpour and A. Ghorbani (2017) as a generalization of Artnian rings. It is of interest to investigate more deeply this class of rings. This study focuses on commutative case. In this vein, we present this work in which we examine the transfer of these rings to the trivial, amalgamation and polynomial ring extensions. We also investigate the relationship between this class of rings...

Left APP-property of formal power series rings

Zhongkui Liu, Xiao Yan Yang (2008)

Archivum Mathematicum

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A ring R is called a left APP-ring if the left annihilator l R ( R a ) is right s -unital as an ideal of R for any element a ∈ R . We consider left APP-property of the skew formal power series ring R [ [ x ; α ] ] where α is a ring automorphism of R . It is shown that if R is a ring satisfying descending chain condition on right annihilators then R [ [ x ; α ] ] is left APP if and only if for any sequence ( b 0 , b 1 , ⋯ ) of elements of R the ideal l R ( ∑ j = 0 ∞ ∑ k = 0 ∞ R α k ( b j ) ) is right s -unital. As an application we give a sufficient condition under which...

A note on semilocal group rings

Angelina Y. M. Chin (2002)

Czechoslovak Mathematical Journal

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Let R be an associative ring with identity and let J ( R ) denote the Jacobson radical of R . R is said to be semilocal if R / J ( R ) is Artinian. In this paper we give necessary and sufficient conditions for the group ring R G , where G is an abelian group, to be semilocal.

Extensions of G M -rings

Huanyin Chen, Miaosen Chen (2005)

Czechoslovak Mathematical Journal

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It is shown that a ring R is a G M -ring if and only if there exists a complete orthogonal set { e 1 , ⋯ , e n } of idempotents such that all e i R e i are G M -rings. We also investigate G M -rings for Morita contexts, module extensions and power series rings.