On modules satisfying S-dccr condition

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Atıf İçin Kopyala

Özen M., Naji O. A., Tekir Ü., Koç S.

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, cilt.2021, ss.1-14, 2021 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 2021
• Basım Tarihi: 2021
• Doi Numarası: 10.1007/s13366-021-00609-9
• Dergi Adı: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
• Sayfa Sayıları: ss.1-14
• Marmara Üniversitesi Adresli: Evet

Özet

In this paper, we introduce a new class of modules satisfying S-dccr (S-dccr⋆)" role="presentation" >⋆)${}^{\star })$ condition which is a generalization of S-artinian modules. Let A " role="presentation" >A $A$be a commutative ring with 0≠1 " role="presentation" >0≠1 $0\ne 1$and X " role="presentation" >X $X$a unital A-module. Suppose that S⊆A " role="presentation" >S⊆A $S\subseteq A$is a multiplicatively closed subset. X " role="presentation" >X $X$is said to satisfy S-dccr (S-dccr⋆)" role="presentation" >⋆)${}^{\star })$ condition if for each finitely generated (principal) ideal I " role="presentation" >I $I$of A " role="presentation" >A $A$and a submodule Y " role="presentation" >Y $Y$of X, " role="presentation" >X, $X,$the descending chain {IiY}i∈N" role="presentation" >{IiY}i∈N$\{I^{i}Y{\}}_{i\in \mathbb{N}}$ is S-stationary. Many examples and properties of modules satisfying S-dccr (S-dccr⋆) " role="presentation" >⋆) ${}^{\star })$condition are given. Furthermore, we characterize modules satisfying dccr (dccr⋆)" role="presentation" >⋆)${}^{\star })$ condition in terms of some known class of rings and modules. Also, we give Nakayama’s Lemma for modules satisfying S-dccr condition.