Some homological properties of amalgamation

Abstract

Let $R$ and $S$ be commutative rings, let $J$ be an ideal of $S$ andlet $f \: R\to S$ be a ring homomorphism. In this paper, weinvestigate some homological properties of the amalgamation of $R$with $S$ along $J$ with respect to $f$ (denoted by $R\bowtie^{f}J$), introduced by D'Anna and Fontana in $2007$. In addition, wedeal with the strongly cotorsion properties of local cohomologymodule of $R\bowtie^{f} J$, when $R\bowtie^{f} J$ is a localNoetherian ring.