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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On the length of a Hilbert ascending chain


Author: A. Seidenberg
Journal: Proc. Amer. Math. Soc. 29 (1971), 443-450
MSC: Primary 13.25
MathSciNet review: 0280473
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Abstract: It is 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 the field $ k,i = 0,1,2, \cdots $, then a bound can be placed on the length of a strictly ascending chain $ {A_0} < {A_1} < \cdots $. Moreover one could explicitly write down a formula for a bound $ {g_n}$ in terms of f and n.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0280473-X
PII: S 0002-9939(1971)0280473-X
Keywords: Polynomial rings, ideal chains
Article copyright: © Copyright 1971 American Mathematical Society