On weakly $n$-absorbing ideals of commutative rings

TL;DR

This paper explores weakly n-absorbing ideals in commutative rings, generalizing previous concepts, and confirms conjectures in the context of u-rings, advancing the theoretical understanding of ideal structures.

Contribution

It extends the theory of weakly n-absorbing ideals, proving conjectures and questions for u-rings, thus broadening the scope of ideal theory in commutative algebra.

Findings

Conjectures about n-absorbing ideals hold in u-rings.

Weakly 2-absorbing ideals are generalized to weakly n-absorbing ideals.

Theoretical results confirm existing conjectures in a new class of rings.

Abstract

All rings are commutative with $1\neq0$. The purpose of this paper is to investigate the concept of weakly $n$-absorbing ideals generalizing weakly 2-absorbing ideals. We prove that over a $u$-ring $R$ the Anderson-Badawi's conjectures about $n$-absorbing ideals and the Badawi-Yousefian's question about weakly 2-absorbing ideals hold.