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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Construction of the integral closure of a finite integral domain. II
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by A. Seidenberg PDF
Proc. Amer. Math. Soc. 52 (1975), 368-372 Request permission

Abstract:

In a previous paper the problem of constructing the integral closure of a finite integral domain $k[{x_1}, \ldots ,{x_n}] = k[x]$ was considered. A reduction to the case $dtk(x)/k = 1,k(x)/k$ separable, and $n = 2$ was made. A subsidiary problem was: if $k[x]$ is not integrally closed, to find a $y$ in $k(x)$ integral over $k[x]$ but not in it. This was done for $n = 2$, but should have been done for arbitrary $n$. The extra details are here given. For the convenience of the reader, the full argument is sketched.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 368-372
  • MSC: Primary 13B20; Secondary 02E99
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0424783-5
  • MathSciNet review: 0424783