Weakly classical 1-absorbing primary submodules

In this paper, we introduce weakly classical 1-absorbing primary submodules of an unital module over a commutative ring with nonzero identity. Consider [Formula: see text] as a module over a ring [Formula: see text]. A proper submodule [Formula: see text] of [Formula: see text] is called weakly classical 1-absorbing primary submodule, if for each nonunit [Formula: see text] and [Formula: see text] with [Formula: see text], it follows that either [Formula: see text] or [Formula: see text] for some [Formula: see text]. Various properties and characterizations of weakly classical 1-absorbing primary submodules are explored.

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Publication Details

Journal
Asian-European Journal of Mathematics
Published
2026-01-30
DOI
https://doi.org/10.1142/s1793557126500142
Primary Topic
Rings, Modules, and Algebras
Type
article
Field-Weighted Citation Impact
0.00
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article

Weakly classical 1-absorbing primary submodules

Bayram Alì Ersoy, Serkan Onar, Ece Yetki̇n Çeli̇kel, Unsal Tekir et al.
Asian-European Journal of Mathematics
Rings, Modules, and Algebras
article

Weakly classical 1-absorbing primary submodules

Bayram Alì Ersoy, Serkan Onar, Ece Yetki̇n Çeli̇kel, Unsal Tekir, Zeynep Yilmaz Ucar
article en

Abstract

In this paper, we introduce weakly classical 1-absorbing primary submodules of an unital module over a commutative ring with nonzero identity. Consider [Formula: see text] as a module over a ring [Formula: see text]. A proper submodule [Formula: see text] of [Formula: see text] is called weakly classical 1-absorbing primary submodule, if for each nonunit [Formula: see text] and [Formula: see text] with [Formula: see text], it follows that either [Formula: see text] or [Formula: see text] for some [Formula: see text]. Various properties and characterizations of weakly classical 1-absorbing primary submodules are explored.

Asian-European Journal of Mathematics
Yıldız Technical University (TR), Hasan Kalyoncu University (TR), Marmara University (TR), Software (Spain) (ES)
Openalex Percentile: Top 66%
Rings, Modules, and Algebras
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