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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Eisenbud-Evans generalized principal ideal theorem and determinantal ideals


Author: Winfried Bruns
Journal: Proc. Amer. Math. Soc. 83 (1981), 19-24
MSC: Primary 13C05; Secondary 13C15
MathSciNet review: 619972
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Abstract: In [2] Eisenbud and Evans gave an important generalization of Krull's Principal Ideal Theorem. However, their proof, using maximal Cohen-Macaulay modules, may have limited the validity of their theorem to a proper subclass of all local rings. (Hochster proved the existence of maximal Cohen-Macaulay modules for local rings which contain a field, cf. [4]). In the first section we present a proof which is simpler and guarantees the Generalized Principal Ideal Theorem for all local rings. The main result of the second section was conjectured in [2]. Under a hypothesis typically being satisfied for the most important fitting invariant of a module, it improves the Eagon-Northcott bound [1] on the height of a determinantai ideal considerably. Finally we will discuss the implications of a recent theorem of Fairings [3] on determinantal ideals.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0619972-3
PII: S 0002-9939(1981)0619972-3
Article copyright: © Copyright 1981 American Mathematical Society