Some properties of $n$-semidualizing modules

TL;DR

This paper explores properties of $n$-semidualizing modules over commutative noetherian rings, establishing foundational results and linking them to divisor class groups in Gorenstein determinantal rings.

Contribution

It introduces and analyzes basic properties of $n$-semidualizing modules, connecting them to divisor class groups in specific algebraic structures.

Findings

Divisor class group of Gorenstein determinantal rings corresponds to 1-semidualizing modules.

Basic properties of $n$-semidualizing modules are established.

Open questions about the structure of $n$-semidualizing modules are posed.

Abstract

Let $R$ be a commutative noetherian ring. The $n$-semidualizing modules of $R$ are generalizations of its semidualizing modules. We will prove some basic properties of $n$-semidualizing modules. Our main result and example 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. Finally, we pose some questions about $n$-semidualizing modules.