Linkage of finite Gorenstein dimension modules

Details Linkage of finite Gorenstein dimension modules Linkage of finite Gorenstein dimension modules

2011-09-29

arxiv.org/abs/1109.6528v2

Mathematics

Commutative Algebra

21 pages, Theorem 2.7 is corrected

Scientific paper

For a horizontally linked module, over a commutative semiperfect Noetherian ring $R$, the connections of its invariants reduced grade, Gorenstein dimension and depth are studied. It is shown that under certain conditions the depth of a horizontally linked module is equal to the reduced grade of its linked module. The connection of the Serre condition $(S_n)$ on an $R$--module of finite Gorenstein dimension with the vanishing of the local cohomology groups of its linked module is discussed.

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