https://handwiki.org/wiki/index.php?title=Zariski%27s_finiteness_theorem&feed=atom&action=historyZariski's finiteness theorem - Revision history2024-03-28T21:51:13ZRevision history for this page on the wikiMediaWiki 1.38.4https://handwiki.org/wiki/index.php?title=Zariski%27s_finiteness_theorem&diff=3384754&oldid=prevCarolyn: simplify2024-02-07T04:30:32Z<p>simplify</p>
<p><b>New page</b></p><div>In algebra, '''Zariski's finiteness theorem''' gives a positive answer to Hilbert's 14th problem for the polynomial ring in two variables, as a special case.<ref>{{cite web|url=http://aix1.uottawa.ca/~ddaigle/articles/H14survey.pdf|title=HILBERT’S FOURTEENTH PROBLEM AND LOCALLY NILPOTENT DERIVATIONS|access-date=2023-08-25}}</ref> Precisely, it states:<br />
:Given a normal domain ''A'', finitely generated as an algebra over a field ''k'', if ''L'' is a subfield of the field of fractions of ''A'' containing ''k'' such that <math>\operatorname{tr.deg}_k(L) \le 2</Math>, then the ''k''-subalgebra <math>L \cap A</math> is finitely generated.<br />
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== References ==<br />
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*{{cite journal|last1=Zariski|first1=O.|title=Interprétations algébrico-géométriques du quatorzième problème de Hilbert|journal=Bull. Sci. Math. (2)|date=1954|volume=78|pages=155–168}}<br />
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[[Category:Hilbert's problems]]<br />
[[Category:Invariant theory]]<br />
[[Category:Commutative algebra]]<br />
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{{Sourceattribution|Zariski's finiteness theorem}}</div>Carolyn