Semidualizing modules and the divisor class group

Details Semidualizing modules and the divisor class group Semidualizing modules and the divisor class group

2004-08-29

arxiv.org/abs/math/0408399v3

Mathematics

Commutative Algebra

30 pages, uses XY-pic and amsart; final version for publication in Illinois J. Math. Griffith volume; extensively rewritten af

Scientific paper

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.

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