Graded weakly 1-absorbing primary ideals

Abstract Let G G be a group and R R -graded commutative ring with nonzero unity 1. In this article, we introduce the concept of graded weakly 1-absorbing primary ideals which is generalization ideal. A proper ideal P P said to if whenever nonunit elements x , y z ∈ h ( ) x,y,z\in h\left(R) such that 0 ≠ 0\ne xyz\in , then xy\in or n {z}^{n}\in for some N n\in {\mathbb{N}} . Several properties are investigated.