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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Commutative extensions by canonical modules are Gorenstein rings


Author: Robert Fossum
Journal: Proc. Amer. Math. Soc. 40 (1973), 395-400
MSC: Primary 13H10
DOI: https://doi.org/10.1090/S0002-9939-1973-0318139-1
MathSciNet review: 0318139
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Abstract: Reiten has demonstrated that the trivial Hochschild extension of a Cohen-Macaulay local ring by a canonical module is a Gorenstein local ring. Here it is proved that any commutative extension of a Cohen-Macaulay local ring by a canonical module is a Gorenstein ring. Also Gorenstein extensions of a local Cohen-Macaulay ring by a module are studied.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0318139-1
Keywords: Noetherian, Gorenstein, Cohen-Macaulay, local ring, canonical module, extension
Article copyright: © Copyright 1973 American Mathematical Society