Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13.25

Retrieve articles in all journals with MSC: 13.25

Additional Information

PII: S 0002-9939(1971)0280473-X
Keywords: Polynomial rings, ideal chains
Article copyright: © Copyright 1971 American Mathematical Society