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Some notes on graded weakly 1-absorbing primary ideals

Alshehry Azzh Saad, Abu-Dawwas Rashid, Al-Rashdan Majd

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20230111

A proper graded ideal P of a commutative graded ring R is called graded weakly 1-absorbing primary if whenever x, y, z are nonunit homogeneous elements of R with 0≠xyz ∈ P , then either xy ∈ P or z is in the graded radical of P. In this article, we explore more results on graded weakly 1-absorbing primary ideals.

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.