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More on the strongly 1-absorbing primary ideals of commutative rings

Ali Yassine, Mohammad Javad Nikmehr, Reza Nikandish (2024)

Czechoslovak Mathematical Journal

Let R be a commutative ring with identity. We study the concept of strongly 1-absorbing primary ideals which is a generalization of n -ideals and a subclass of 1 -absorbing primary ideals. A proper ideal I of R is called strongly 1-absorbing primary if for all nonunit elements a , b , c ∈ R such that a b c ∈ I , it is either a b ∈ I or c ∈ 0 . Some properties of strongly 1-absorbing primary ideals are studied. Finally, rings R over which every semi-primary ideal is strongly 1-absorbing primary, and rings R over which every strongly...

Multiplication modules and related results

Shahabaddin Ebrahimi Atani (2004)

Archivum Mathematicum

Let R be a commutative ring with non-zero identity. Various properties of multiplication modules are considered. We generalize Ohm’s properties for submodules of a finitely generated faithful multiplication R -module (see [8], [12] and [3]).

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