Some properties of \(n\)-semidualizing modules (Q6173997)

In the paper under review the author introduces a generalization of semidualizing modules as follows: Let \(R\) be a commutative Noetherian ring and \(n\in\mathbb{N}\). Then an \(R\)-module \(C\) is called \(n\)-semidualizing if \(\mathrm{Hom}_R(C,C)\cong R\) and \(\mathrm{Ext}^i_R(C, C)=0\) for all \(0 < i \le n\). The author proves some basic properties of \(n\)-semidualizing modules and shows that the divisor class group of a Gorenstein determinantal ring over a field is the set of isomorphism classes of its 1-semidualizing modules.