https://commalg.subwiki.org/w/index.php?action=history&feed=atom&title=Bezout_implies_gcd 2026-10-10T16:43:27Z Revision history for this page on the wiki MediaWiki 1.41.2 https://commalg.subwiki.org/w/index.php?title=Bezout_implies_gcd&diff=80&oldid=prev 2008-05-12T16:18:50Z

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Vipul https://commalg.subwiki.org/w/index.php?title=Bezout_implies_gcd&diff=79&oldid=prev 2008-01-05T21:08:42Z

<p></p> <p><b>New page</b></p><div>{{integral domain property implication}}<br /> <br /> ==Statement==<br /> <br /> ===Property-theoretic statement===<br /> <br /> The [[property of integral domains]] of being a [[Bezout domain]], is stronger than the property of being a [[gcd domain]].<br /> <br /> ==Proof==<br /> <br /> ===Proof outline===<br /> <br /> * Pick two elements in the given [[Bezout domain]]. We need to determine their gcd.<br /> * Consider the ideal generated by these two elements. This is a [[finitely generated ideal]], and by the definition of Bezout domain, is a [[principal ideal]]. Pick a generator for this principal ideal.<br /> * Show that this generator is indeed the gcd of the two elements.</div>

Vipul