2021/01/02 by Rashid Abu-Dawwas, Abu-Dawwas, Rashid
Mathematics · #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2101.01540
Let R be a commutative G-graded ring with a nonzero unity. In this article, we introduce the concept of graded radically principal ideals. A graded ideal I of R is said to be graded radically principal if Grad(I)=Grad(⟨ c⟩) for some homogeneous c∈ R, where Grad(I) is the graded radical of I. The graded ring R is said to be graded radically principal if every graded ideal of R is graded radically principal. We study graded radically principal rings. We prove an analogue of the Cohen theorem, in the graded case, precisely, a graded ring is graded radically principal if and only if every graded prime ideal is graded radically principal. Finally we study the graded radically principal property for the polynomial ring R[X].