Abstract

Let $R$ and $S$ be commutative rings, let $J$ be an ideal of $S$ and let $f \: R\to S$ be a ring homomorphism. In this paper, we investigate 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, we deal with the strongly cotorsion properties of local cohomology module of $R\bowtie^{f} J$, when $R\bowtie^{f} J$ is a local Noetherian ring.

Keywords: amalgamation; strongly cotorsion; local cohomology.

MSC: 13H10

Pages:  254$-$258     

Volume  68 ,  Issue  4 ,  2016