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Graded weakly 1-absorbing primary ideals

Bataineh Malik, Abu-Dawwas Rashid

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20220214

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