@article{10.2307/2038577,
    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 $k{\l}brack X\_i, \cdots, X\_n \rbrack$ 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 $n$.},
    Author = {Seidenberg, A.},
    File = {On the Length of a Hilbert Ascending Chain - seidenberg1971.pdf},
    ISSN = {00029939, 10886826},
    Journal = {Proceedings of the American Mathematical Society},
    Number = {3},
    Pages = {443--450},
    Publisher = {American Mathematical Society},
    Title = {On the Length of a Hilbert Ascending Chain},
    URL = {http://www.jstor.org/stable/2038577},
    Volume = {29},
    Year = {1971},
    bdsk-url-1 = {http://www.jstor.org/stable/2038577},
    date-added = {2021-08-12 16:09:17 +0200},
    date-modified = {2021-08-12 16:09:17 +0200},
    doi = {10.2307/2038577}
}

@article{10.2307/2038577, 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 $k{\l}brack X_i, \cdots, X_n \rbrack$ 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 $n$.}, Author = {Seidenberg, A.}, File = {On the Length of a Hilbert Ascending Chain - seidenberg1971.pdf}, ISSN = {00029939, 10886826}, Journal = {Proceedings of the American Mathematical Society}, Number = {3}, Pages = {443--450}, Publisher = {American Mathematical Society}, Title = {On the Length of a Hilbert Ascending Chain}, URL = {http://www.jstor.org/stable/2038577}, Volume = {29}, Year = {1971}, bdsk-url-1 = {http://www.jstor.org/stable/2038577}, date-added = {2021-08-12 16:09:17 +0200}, date-modified = {2021-08-12 16:09:17 +0200}, doi = {10.2307/2038577} }