Square-difference factor absorbing ideals of a commutative ring

Let $R$ be a commutative ring with $1\mathrm{\ne }0$. 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 $0\mathrm{\ne }a,b\in R$, then $a+b\in I$ or $a-b\in I$. In this paper, we introduce and investigate sdf-absorbing ideals.