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Proceedings of the American Mathematical Society

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

 

 

Construction of the integral closure of a finite integral domain. II


Author: A. Seidenberg
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1975-0424783-5
Keywords: Constructive mathematics, finite integral domain, integral closure
Article copyright: © Copyright 1975 American Mathematical Society