$n$-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.References
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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