In this paper, we introduce and study the concept of strongly dccr⋆ modules. Strongly dccr⋆ condition generalizes the class of Artinian modules and it is stronger than dccr⋆ condition. Let R be a commutative ring with nonzero identity and M a unital R-module. A module M is said to be strongly dccr⋆ if for every submodule N of M and every sequence of elements (ai) of R, the descending chain of submodules a1N⊇a1a2N⊇⋯⊇a1a2…anN⊇⋯ of M is stationary. We give many examples and properties of strongly dccr⋆. Moreover, we characterize strongly dccr⋆ in terms of some known class of rings and modules, for instance in perfect rings, strongly special modules and principally cogenerately modules. Finally, we give a version of Union Theorem and Nakayama’s Lemma in light of strongly dccr⋆ concept.
展开▼
