On the length of a Hilbert ascending chain
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- by A. Seidenberg
- Proc. Amer. Math. Soc. 29 (1971), 443-450
- DOI: https://doi.org/10.1090/S0002-9939-1971-0280473-X
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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.References
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Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 443-450
- MSC: Primary 13.25
- DOI: https://doi.org/10.1090/S0002-9939-1971-0280473-X
- MathSciNet review: 0280473