Semidualizing modules and the divisor class group
Commutative Algebra
2007-05-23 v3 Rings and Algebras
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.
Cite
@article{arxiv.math/0408399,
title = {Semidualizing modules and the divisor class group},
author = {Sean Sather-Wagstaff},
journal= {arXiv preprint arXiv:math/0408399},
year = {2007}
}
Comments
30 pages, uses XY-pic and amsart; final version for publication in Illinois J. Math. Griffith volume; extensively rewritten after referee's comments