https://commalg.subwiki.org/w/index.php?action=history&feed=atom&title=Free_ideal_ringFree ideal ring - Revision history2026-10-30T19:19:02ZRevision history for this page on the wikiMediaWiki 1.41.2https://commalg.subwiki.org/w/index.php?title=Free_ideal_ring&diff=333&oldid=prevVipul: 1 revision2008-05-12T16:21:50Z<p>1 revision</p>
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</td></tr></table>Vipulhttps://commalg.subwiki.org/w/index.php?title=Free_ideal_ring&diff=332&oldid=prevVipul: /* Stronger properties */2007-01-09T05:31:16Z<p><span dir="auto"><span class="autocomment">Stronger properties</span></span></p>
<p><b>New page</b></p><div>==Definition for commutative rings==<br />
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===Symbol-free definition===<br />
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A [[commutative unital ring]] (or any [[commutative ring]]) is termed a '''free ideal ring''' or '''fir''' if every ideal of that ring is a [[free module]] as a module over that ring.<br />
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==Definition for noncommutative rings==<br />
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For noncommutative rings, there are two notions:<br />
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* [[Free left ideal ring]] or '''left fir'''<br />
* [[Free right ideal ring]] or '''right fir'''<br />
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==Relation with other properties==<br />
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===Stronger properties===<br />
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* [[Field]]<br />
* [[Principal ideal domain]]<br />
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===Weaker properties===<br />
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* [[Integral domain]]<br />
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[[Category: Properties of commutative rings]]<br />
[[Category: Properties of integral domains]]</div>Vipul