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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Constructive proof of Hilbert's theorem on ascending chains


Author: A. Seidenberg
Journal: Trans. Amer. Math. Soc. 174 (1972), 305-312
MSC: Primary 13E10; Secondary 02E99
MathSciNet review: 0314829
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Abstract: In a previous note it was shown that if a bound $ f(i)$ is placed on the degrees of the elements in some basis of an ideal $ {A_i}$ in the polynomial ring $ k[{X_1}, \cdots ,{X_n}]$ over an explicitly given field $ k,i = 0,1,2, \cdots $, then a bound can be (and was) constructed for the length of a strictly ascending chain $ {A_0} < {A_1} < \cdots $. This result is now obtained using a strictly finitist argument. A corollary is a finitist version of Hilbert's theorem on ascending chains.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0314829-9
PII: S 0002-9947(1972)0314829-9
Keywords: Constructive mathematics, polynomial ideals, ascending chain condition
Article copyright: © Copyright 1972 American Mathematical Society