On graded 1-absorbing prime ideals - KOÇ, SUAT; TEKİR, ÜNSAL (SPRINGER INTERNATIONAL PUBLISHING AG, 2021)
Let G be a group with identity e and R be a G-graded commutative ring with unity 1. In this article, we introduce and study the concept of graded 1-absorbing prime ideals which is a generalization of graded prime ideals. A proper graded ideal P of R is called graded 1-absorbing prime if for all nonunit elements x,y,z is an element of h(R) such that xy z is an element of P, then either xy is an element of P or z is an element of P.
Keywords: Graded 1-absorbing prime ideal; Graded prime ideal; Graded primary ideal; Graded 2-absorbing ideal