https://galois.subwiki.org/w/index.php?action=history&feed=atom&title=Cyclotomic_extension 2026-07-14T23:37:58Z Revision history for this page on the wiki MediaWiki 1.41.2 https://galois.subwiki.org/w/index.php?title=Cyclotomic_extension&diff=85&oldid=prev 2009-05-15T01:32:16Z

<p>Created page with &#039;{{field extension property}} ==Definition== A <a href="/w/index.php?title=Field_extension&amp;action=edit&amp;redlink=1" class="new" title="Field extension (page does not exist)">field extension</a> is termed a &#039;&#039;&#039;cyclotomic extension&#039;&#039;&#039; if it is obtained as the splitting field of polynomials of the form &lt;ma...&#039;</p> <p><b>New page</b></p><div>{{field extension property}}<br /> <br /> ==Definition==<br /> <br /> A [[field extension]] is termed a &#039;&#039;&#039;cyclotomic extension&#039;&#039;&#039; if it is obtained as the splitting field of polynomials of the form &lt;math&gt;x^n - 1&lt;/math&gt;, where &lt;math&gt;n&lt;/math&gt; is not a multiple of the characteristic of the field. In other words, it is an extension obtained by adjoining primitive &lt;math&gt;n^{th}&lt;/math&gt; roots of unity.</div>

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