English

On Graded s-Prime Submodules

Rings and Algebras 2020-09-15 v2 Commutative Algebra

Abstract

In this article, we introduce the concepts of graded ss-prime submodules which is a generalization of graded prime submodules. We study the behavior of this notion with respect to graded homomorphisms, localization of graded modules, direct product, and idealization. We succeeded to prove the existence of graded ss-prime submodules in the case of graded-Noetherian modules. Also, we provide some sufficient conditions for the existence of such objects in the general case, as well as, in the particular case of grading by Z\mathbb{Z}, a finite group, or a polycyclic-by-finite group, in addition to crossed product grading.

Keywords

Cite

@article{arxiv.2008.05529,
  title  = {On Graded s-Prime Submodules},
  author = {Hicham Saber and Tariq Alraqad and Rashid Abu-Dawwas},
  journal= {arXiv preprint arXiv:2008.05529},
  year   = {2020}
}
R2 v1 2026-06-23T17:49:01.177Z