Ontology type: schema:ScholarlyArticle
2021-09-23
AUTHORST. H. Freitas, V. H. Jorge Pérez
ABSTRACTFoxby (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... »
PAGES485-494
http://scigraph.springernature.com/pub.10.1007/s00013-021-01659-0
DOIhttp://dx.doi.org/10.1007/s00013-021-01659-0
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