Year: 2020
Type: article
Abstract: In this article, we introduce the concepts of graded $ s $-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 $ s $-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 a grading by a finite group, polycyclic-by-finite group, or by $ \mathbb{Z} $, in addition to the interesting case of crossed product grading, which includes the class of group rings.
Source: AIMS Mathematics
DOI: 10.3934/math.2021152
Authors: Hicham Saber, Tariq Alraqad, Rashid Abu-Dawwas
Institutions: University of Ha'il, Yarmouk University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,200
OpenAlex ID: W3048752384