Characterizations and Transfer Properties of Graded N-Prime Ideals in Graded Rings

Abstract

This paper introduces the notion of graded N-prime ideals as a natural bridge between graded prime ideals and graded quasi-primary ideals within the framework of G graded commutative rings, where G is a group. We investigate their fundamental properties and characterizations, focusing on their behavior under graded ring constructions such as localization, factor rings, and trivial extensions. Several equivalences and transfer properties are established, offering a comprehensive understanding of graded N-prime ideals. Illustrative examples highlight their distinctions from other generalized ideals and emphasize their intermediate nature. Furthermore, we characterize graded rings in which every graded ideal is a graded N-prime ideal.