When does the canonical module of a module have finite injective dimension? View Full Text


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Article Info

DATE

2021-09-23

AUTHORS

T. H. Freitas, V. H. Jorge Pérez

ABSTRACT

Foxby (Math Scand 2:175–186, 1971–1972) showed that a Cohen-Macaulay module over a Gorenstein local ring has finite projective dimension if and only if its canonical module has finite injective dimension. In this paper, we establish the result given by Foxby in a general setting. As a byproduct, some criteria to detect the Cohen-Macaulay property of a ring are provided in terms of intrinsic properties of certain local cohomology modules. Also, as an application, we show that any Cohen-Macaulay module that has a canonical module with finite injective dimension satisfies the Auslander–Reiten conjecture. More... »

PAGES

485-494

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00013-021-01659-0

DOI

http://dx.doi.org/10.1007/s00013-021-01659-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1141327577


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