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 not equal 0. A proper graded ideal P of R is called a graded weakly 1-absorbing prime ideal if for each nonunits x, y, z is an element of h(R) with 0 not equal= xyz is an element of P, then either xy. P or z is an element of 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.