Semidualizing modules and the divisor class group
S Sather-Wagstaff - Illinois Journal of Mathematics, 2007 - projecteuclid.org
Illinois Journal of Mathematics, 2007•projecteuclid.org
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 …
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 …
Among the finitely generated modules over a Noetherian ring , the semidualizing modules have been singled out due to their particularly nice duality properties. When is a normal domain, we exhibit a natural inclusion of the set of isomorphism classes of semidualizing -modules into the divisor class group of . 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 -modules. In particular, this set is described completely for determinantal rings over normal domains.
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