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$ n$-Gorenstein rings


Author: Hans Bjørn Foxby
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
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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

DOI: https://doi.org/10.1090/S0002-9939-1974-0323784-4
Keywords: $ ({{\text{a}}_n})$- and $ ({{\text{b}}_n})$-module, nth syzgy, module without n-torsion
Article copyright: © Copyright 1974 American Mathematical Society

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