Semidualizing modules and the divisor class group
Semidualizing modules and the divisor class group
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DOI：
10.1215/ijm/1258735335
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发表时间：
2004-08
影响因子：
0.6
通讯作者：
S. Sather-Wagstaff
中科院分区：
文献类型：
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作者：
S. Sather-Wagstaff
在Noether环R上的有限生成模中，半对偶模由于其特殊的对偶性质而被挑出来。当R是正规整环时，我们证明了半对偶化R-模的同构类集到R的除数类群中的自然包含，在描述了这种包含的基本性质之后，利用它研究了半对偶R-模的同构类集的结构。特别地，对于正规整环上的行列式环，完整地刻画了这一集合。
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.