On modules satisfying S-dccr condition


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)

Özet

In this paper, we introduce a new class of modules satisfying S-dccr (S-dccr⋆)" role="presentation" >) condition which is a generalization of S-artinian modules. Let A " role="presentation" >A be a commutative ring with 0≠1 " role="presentation" >01 and X " role="presentation" >X a unital A-module. Suppose that S⊆A " role="presentation" >SA is a multiplicatively closed subset. X " role="presentation" >X is said to satisfy S-dccr (S-dccr⋆)" role="presentation" >) condition if for each finitely generated (principal) ideal I " role="presentation" >I of A " role="presentation" >A and a submodule Y " role="presentation" >Y of X, " role="presentation" >X, the descending chain {IiY}i∈N" role="presentation" >{IiY}iN is S-stationary. Many examples and properties of modules satisfying S-dccr (S-dccr⋆) " role="presentation" >) condition are given. Furthermore, we characterize modules satisfying dccr (dccr⋆)" role="presentation" >) condition in terms of some known class of rings and modules. Also, we give Nakayama’s Lemma for modules satisfying S-dccr condition.