Square-difference factor absorbing ideals of a commutative ring

TL;DR

This paper introduces and investigates square-difference factor absorbing ideals in commutative rings, exploring their properties and implications within ring theory.

Contribution

It defines sdf-absorbing ideals and studies their characteristics, expanding the understanding of ideal structures in commutative rings.

Findings

Characterization of sdf-absorbing ideals

Conditions under which ideals are sdf-absorbing

Examples illustrating the concept

Abstract

Let $R$ be a commutative ring with $1 \neq 0$. A proper ideal $I$ of $R$ is a {\it square-difference factor absorbing ideal} (sdf-absorbing ideal) of $R$ if whenever $a^2 - b^2 \in I$ for $0 \neq a, b \in R$, then $a + b \in I$ or $a - b \in I$. In this paper, we introduce and investigate sdf-absorbing ideals.