https://commalg.subwiki.org/w/index.php?action=history&feed=atom&title=Purely_transcendental_field_extensionPurely transcendental field extension - Revision history2026-05-31T16:07:11ZRevision history for this page on the wikiMediaWiki 1.41.2https://commalg.subwiki.org/w/index.php?title=Purely_transcendental_field_extension&diff=1061&oldid=prevVipul: 1 revision2008-05-12T16:33:48Z<p>1 revision</p>
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</td></tr></table>Vipulhttps://commalg.subwiki.org/w/index.php?title=Purely_transcendental_field_extension&diff=1060&oldid=prevVipul: New page: {{field extension property}} ==Definition== Let <math>k</math> be a field and <math>K</math> be a field extension of <math>k</math> (i.e. a field containing <math>k</math>). Then, we...2008-02-08T22:24:52Z<p>New page: {{field extension property}} ==Definition== Let <math>k</math> be a <a href="/wiki/Field" title="Field">field</a> and <math>K</math> be a field extension of <math>k</math> (i.e. a field containing <math>k</math>). Then, we...</p>
<p><b>New page</b></p><div>{{field extension property}}<br />
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==Definition==<br />
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Let <math>k</math> be a [[field]] and <math>K</math> be a field extension of <math>k</math> (i.e. a field containing <math>k</math>). Then, we say that <math>K</math> is a purely transcendental field extension of <math>k</math>, if there exists a subset <math>T</math> of <math>K</math> such that <math>T</math> is algebraically independent over <math>k</math>, and the naturally induced map from the field of fractions <math>k(T)</math> to <math>K</math> is an isomorphism.</div>Vipul