A GENERALIZATION OF SEMINOETHERIAN RINGS AND MODULES

Document Type : Original Manuscript

Authors

Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

10.22044/jas.2025.14717.1855

Abstract

We study those modules in which all submodules contain a nonzero submodule with Noetherian dimension less than or equal to $\alpha $ where $\alpha $ is the least ordinal number with this property, calling them modules that have enough $\alpha$-noetherians. Also, we study those modules in which any nonzero factor module contains a nonzero submodule with Noetherian dimension less than or equal to $\alpha$, where $\alpha$ is the least ordinal number with this property, calling them $\alpha$-seminoetherians. Our work extends the results of Kourki and Tribak in Commu. Algebra (2022).

Keywords

References

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Journal of Algebraic Systems
Volume 14, Issue 3
June 2026
Pages 531-547

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