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Proceedings of the American Mathematical Society

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

 
 

 

The existence of minimal regular local overrings for an arbitrary domain


Author: Bernard Johnston
Journal: Proc. Amer. Math. Soc. 100 (1987), 419-423
MSC: Primary 13H05
DOI: https://doi.org/10.1090/S0002-9939-1987-0891138-7
MathSciNet review: 891138
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Abstract: It is shown that the set of regular local rings of dimension $ n$ containing an integral domain $ D$, having the same quotient field as $ D$, and ordered by containment satisfies the descending chain condition. The set of regular local rings of dimension $ n$ contained in a regular local ring of dimension $ m,n > m$, need not satisfy the ascending chain condition, as is shown by example.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0891138-7
Keywords: Birational, regular local ring, quadratic transform, descending chain condition
Article copyright: © Copyright 1987 American Mathematical Society

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