Abstract
If M is a nonzero finitely generated module over a commutative Noetherian local ring R such that M has finite injective dimension and finite Gorenstein dimension, then it follows from a result of Holm that M has finite projective dimension, and hence a result of Foxby implies that R is Gorenstein. We prove that the same conclusion holds for certain nonzero finitely generated modules that have finite injective dimension and finite reducing Gorenstein dimension, where the reducing Gorenstein dimension is a finer invariant than the classical Gorenstein dimension, in general. Along the way, we also prove new results, independent of the reducing dimensions, concerning modules of finite Gorenstein dimension.
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Schedule a callMore From: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
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