مجله مدل‌سازی پیشرفته ریاضی

مجله مدل‌سازی پیشرفته ریاضی

Modules with Dual enough Noetherians

نوع مقاله : اصیل

نویسندگان
1 ,Department of Mathematics Faculty of Mathematical Sciences and Computer , Shahid Chamran University of Ahvaz, Ahvaz, Iran
2 Department of Mathematics , Faculty of Mathematical Sciences and Computer Shahid Chamran University of Ahvaz,, Ahvaz, Iran,
چکیده
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 (2022). 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.
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موضوعات

  • تاریخ دریافت 18 اسفند 1403
  • تاریخ بازنگری 28 دی 1404
  • تاریخ پذیرش 24 خرداد 1405