Displaying similar documents to “A note on semilocal group rings”

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.

On a theorem of McCoy

Rajendra K. Sharma, Amit B. Singh (2024)

Mathematica Bohemica

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We study McCoy’s theorem to the skew Hurwitz series ring ( HR , ω ) for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings. Moreover, we establish an equivalence relationship between a right zip ring and its skew Hurwitz series ring in case when a ring R satisfies McCoy’s theorem of skew Hurwitz series.

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...

When is every order ideal a ring ideal?

Melvin Henriksen, Suzanne Larson, Frank A. Smith (1991)

Commentationes Mathematicae Universitatis Carolinae

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A lattice-ordered ring ℝ is called an if each of its order ideals is a ring ideal. Generalizing earlier work of Basly and Triki, OIRI-rings are characterized as those f -rings ℝ such that ℝ / 𝕀 is contained in an f -ring with an identity element that is a strong order unit for some nil l -ideal 𝕀 of ℝ . In particular, if P ( ℝ ) denotes the set of nilpotent elements of the f -ring ℝ , then ℝ is an OIRI-ring if and only if ℝ / P ( ℝ ) is contained in an f -ring with an identity element that is a strong order unit. ...