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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]).

Noetherian loop spaces

Natàlia Castellana, Juan Crespo, Jérôme Scherer (2011)

Journal of the European Mathematical Society

The class of loop spaces of which the mod p cohomology is Noetherian is much larger than the class of p -compact groups (for which the mod p cohomology is required to be finite). It contains Eilenberg–Mac Lane spaces such as ℂ P ∞ and 3-connected covers of compact Lie groups. We study the cohomology of the classifying space B X of such an object and prove it is as small as expected, that is, comparable to that of B ℂ P ∞ . We also show that B X differs basically from the classifying space of a p -compact group...

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