https://commalg.subwiki.org/w/index.php?action=history&feed=atom&title=Intersection_of_prime_equals_radical 2026-07-30T15:22:06Z Revision history for this page on the wiki MediaWiki 1.41.2 https://commalg.subwiki.org/w/index.php?title=Intersection_of_prime_equals_radical&diff=553&oldid=prev 2008-05-12T16:23:56Z

<p>1 revision</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <tr class="diff-title" lang="en"> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:23, 12 May 2008</td> </tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div> </td></tr></table>

Vipul https://commalg.subwiki.org/w/index.php?title=Intersection_of_prime_equals_radical&diff=552&oldid=prev 2008-02-08T23:48:14Z

<p>New page: {{curing property implication}} ==Statement== An <a href="/wiki/Ideal" title="Ideal">ideal</a> in a <a href="/wiki/Commutative_unital_ring" title="Commutative unital ring">commutative unital ring</a> is <a href="/wiki/Radical_ideal" title="Radical ideal">radical</a> if and only if it is an intersection of <a href="/wiki/Prime_ideal" title="Prime ideal">prime ideals</a>. ==Proo...</p> <p><b>New page</b></p><div>{{curing property implication}}<br /> <br /> ==Statement==<br /> <br /> An [[ideal]] in a [[commutative unital ring]] is [[radical ideal|radical]] if and only if it is an intersection of [[prime ideal]]s.<br /> <br /> ==Proof==<br /> <br /> Because of the way the properties are quotient-determined, we can reduce this to the statement that:<br /> <br /> [[nilradical equals intersection of all prime ideals]]</div>

Vipul