Amalgamated rings with clean-type properties

Abstract

Let $f:A\rightarrow B$ be a ring homomorphism and $K$ be an ideal of $B$. Many variations of the notions of clean and nil-clean rings have been studied by a variety of authors. We investigate strongly $\pi$-regular and clean-like properties of the amalgamation ring $A\bowtie^{f}K$ of $A$ with $B$ along $K$ with respect to $f$.