Cohen-Macaulay and Gorenstein properties under the amalgamated construction

Abstract

Let $A$ and $B$ be commutative rings with unity, $f:A\to B$ a ring homomorphism and $J$ an ideal of $B$. Then the subring $A{\bowtie }^{f}J:=\{(a,f(a)+j)|a\in A$ and $j\in J\}$ of $A\times B$ is called the amalgamation of $A$ with $B$ along with $J$ with respect to $f$. In this paper, among other things, we investigate the Cohen-Macaulay and (quasi-)Gorenstein properties on the ring $A{\bowtie }^{f}J$.

13 pages, final version

References in corpus (3)

• Amalgamated algebras along an ideal
• Edge-signed graphs with smallest eigenvalue greater than -2
• Algebraic and topological properties of an amalgamated algebra along an ideal