Square-Difference Factor Absorbing Primary Ideals of Commutative Rings

Let $R$ be a commutative ring with identity. A proper ideal $I$ of a ring $R$ is called a square-difference factor absorbing primary ideal of $R$ if for $a,b\in R$, whenever $a^{2}-b^{2}\in I$, then $a+b\in\sqrt{I}$ or $a-b\in I$. Several characterizations and properties of this class of ideals are presented.Various examples are provided to illustrate the obtained results and demonstrate the applicability of our findings. Furthermore, the properties of this class of ideals are investigated in extensions of rings.