A new characterization of Cohen-Macaulay rings (Q2878799)

The paper under review gives a new characterization of Cohen-Macaulay local rings: A local Noetherian ring \(R\) is a Cohen-Macaulay ring if and only if NEWLINE\[NEWLINE\mathrm{Hom}_R(R/\mathfrak a, R/\mathfrak b)\cong R/\mathfrak aNEWLINE\]NEWLINE for any parameter ideals \(\mathfrak a\) and \(\mathfrak b\) of \(R\) with \(\mathfrak b \subseteq \mathfrak a\). As a consequence, the paper obtain that a local Noetherian ring \(R\) is Gorenstein if and only if every parameter ideal of \(R\) is irreducible.