Non-Graded Ideals and Gorenstein Quotient Rings

Abstract

This paper explores the existence and classification of non-graded ideals in commutative rings, focusing on those whose quotient rings are Gorenstein. While previous works have thoroughly examined graded ideals with Gorenstein quotients, the non-graded case presents unique algebraic challenges and phenomena. We investigate conditions under which non-graded ideals yield Gorenstein quotient rings , and discuss their structural properties. Our results indicate that, under specific algebraic constraints, the collection of non-graded ideals can, depending on the characteristics of the ambient ring.