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Contracted ideals from integral extensions of regular rings

Published online by Cambridge University Press:  22 January 2016

M. Hochster
M. Hochster*
Affiliation:
University of Minnesota
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0. Introduction. The purpose of this paper is to consider the following question: if R is a regular Noetherian ring and S ⊃ R is a module-finite R-algebra, is R a direct summand of S as R-modules? An affirmative answer is given if R contains a field, and it is shown that if the completions of the local rings of S possess maximal Cohen-Macaulay modules in the sense of § 1 of [6] then the conclusion is valid in this case too. Hence, if Conjecture E of [6] is true then the question raised here has an affirmative answer without further restriction on the regular Noetherian ring R, and it will be shown here that only a greatly weakened version of Conjecture E is needed.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 51 , September 1973 , pp. 25 - 43
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

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