Graded Weakly prime Ideals of Non-Commutative Rings
Azzh Saad Alshehry, Rashid Abu-Dawwas
TL;DR
This paper explores the structure of graded weakly prime ideals in non-commutative rings, introducing new concepts and properties, and examining conditions under which all graded ideals are weakly prime.
Contribution
It introduces the study of graded weakly total prime ideals and characterizes rings where all graded ideals are weakly total prime.
Findings
Characterization of rings with all graded ideals weakly prime
Introduction of graded weakly total prime ideals
Examples supporting the theoretical propositions
Abstract
In this article, we consider the structure of graded rings, not necessarily commutative nor with unity, and study the graded weakly prime ideals. We investigate the graded rings in which all graded ideals are graded weakly prime. Several properties are given, and several examples to support given propositions are constructed. We initiate the study of graded weakly total prime ideals and investigate graded rings for which every proper graded ideal is graded weakly total prime.
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