Graded weakly 1-absorbing prime ideals

Abstract

In this paper, we introduce and study graded weakly 1-absorbing prime ideals in graded commutative rings. Let $G$ be a group and $R$ be a $G$-graded commutative ring with a nonzero identity $1\neq0$. A proper graded ideal $P$ of $R$ is called a graded weakly 1-absorbing prime ideal if for each nonunits $x,y,z\in h(R)$ with $0\neq xyz\in P$, then either $xy\in P$ or $z\in P$. We give many properties and characterizations of graded weakly 1-absorbing prime ideals. Moreover, we investigate weakly 1-absorbing prime ideals under homomorphism, in factor ring, in rings of fractions, in idealization.

Keywords

• graded ideal
• 1-absorbing prime ideal
• weakly 1-absorbing prime ideal
• graded weakly 1-absorbing prime ideal