On the length of a Hilbert ascending chain

Seidenberg, A.

doi:10.1090/S0002-9939-1971-0280473-X

On the length of a Hilbert ascending chain
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by A. Seidenberg PDF

Proc. Amer. Math. Soc. 29 (1971), 443-450 Request permission

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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