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arXiv · 2103.00253

On modules with finite reducing Gorenstein dimension

Tokuji Araya·Olgur Celikbas·Jesse Cook·Toshinori Kobayashi
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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 investigate whether the same conclusion holds for 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.

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Tokuji Araya, Olgur Celikbas, Jesse Cook, Toshinori Kobayashi. 2021-02-27. On modules with finite reducing Gorenstein dimension. https://doi.org/10.1007/s13366-023-00687-x

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