Modules with Dual enough Noetherians

In this paper, we investigate a class of modules in which every factor module has a nonzero Artinian factor module, referring to them as {\it modules with dual enough Noetherians}. Additionally, we introduce and study dual seminoetherian modules, which are modules where every nonzero submodule has a nonzero Artinian factor module. Our work serves as a dual counterpart to the results of Kourki and Tribak in Communications in Algebra (۲۰۲۲). We establish several properties of these classes of modules. Notably, we prove that the class of modules with dual enough Noetherians is closed under factor modules, while the class of dual seminoetherian modules is closed under submodules. These findings contribute to the broader structural theory of module categories and extend existing duality principles in module theory.

کلیدواژه ها:

Krull dimension ، Noetherian dimension ، Artinian modules ، Max modules