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Semidualizing modules and the divisor class group. (English) Zbl 1127.13007

From author’s 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.

MSC:

13C05 Structure, classification theorems for modules and ideals in commutative rings
13C13 Other special types of modules and ideals in commutative rings
13C20 Class groups
13C40 Linkage, complete intersections and determinantal ideals
13D05 Homological dimension and commutative rings
13D25 Complexes (MSC2000)
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