Clean property in amalgamated algebras along an ideal

Abstract

Let $f:A\rightarrow B$ be a be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we give a characterization for the amalgamation of $A$ with $B$ along $J$ with respect to $f$(denoted by $R$ $\bowtie^{f}$ $J$) to be (uniquely) clean.