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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$n$-Gorenstein rings
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by Hans Bjørn Foxby PDF
Proc. Amer. Math. Soc. 42 (1974), 67-72 Request permission

Abstract:

The object of this note is to study commutative noetherian n-Gorenstein rings. The first result is: if each module satisfying Samuel’s conditions $({{\text {a}}_i})$ for some $i \leqq n$ is an ith syzygy, then the ring is n-Gorenstein. This is the converse to a theorem of Ischebeck. The next result characterizes n-Gorenstein rings in terms of commutativity of certain rings of endomorphisms. This answers a question of Vasconcelos. Finally the last result deals with embedding of finitely generated modules into finitely generated modules of finite projective dimension.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 42 (1974), 67-72
  • MSC: Primary 13H10
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0323784-4
  • MathSciNet review: 0323784