Semidualizing modules and the divisor class group

Abstract

Among the finitely generated modules over a Noetherian ring $R$, the semidualizing modules have been singled out due to their particularly nice duality properties. When $R$ is a normal domain, we exhibit a natural inclusion of the set of isomorphism classes of semidualizing $R$-modules into the divisor class group of $R$. After a description of the basic properties of this inclusion, it is employed to investigate the structure of the set of isomorphism classes of semidualizing $R$-modules. In particular, this set is described completely for determinantal rings over normal domains.