Illinois Journal of Mathematics

Semidualizing modules and the divisor class group

Sean Sather-Wagstaff

Full-text: Open access

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.

Article information

Source
Illinois J. Math., Volume 51, Number 1 (2007), 255-285.

Dates
First available in Project Euclid: 20 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258735335

Digital Object Identifier
doi:10.1215/ijm/1258735335

Mathematical Reviews number (MathSciNet)
MR2346197

Zentralblatt MATH identifier
1127.13007

Subjects
Primary: 13C20: Class groups [See also 11R29]
Secondary: 13C05: Structure, classification theorems 13C13: Other special types 13C40: Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12]

Citation

Sather-Wagstaff, Sean. Semidualizing modules and the divisor class group. Illinois J. Math. 51 (2007), no. 1, 255--285. doi:10.1215/ijm/1258735335. https://projecteuclid.org/euclid.ijm/1258735335


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