https://commalg.subwiki.org/w/index.php?action=history&feed=atom&title=Chinese_remainder_theoremChinese remainder theorem - Revision history2026-05-05T18:50:42ZRevision history for this page on the wikiMediaWiki 1.41.2https://commalg.subwiki.org/w/index.php?title=Chinese_remainder_theorem&diff=126&oldid=prevVipul: 1 revision2008-05-12T16:19:11Z<p>1 revision</p>
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</td></tr></table>Vipulhttps://commalg.subwiki.org/w/index.php?title=Chinese_remainder_theorem&diff=125&oldid=prevVipul: New page: {{indispensable lemma}} ==Statement== Suppose <math>I_1, I_2, \ldots, I_n</math> are ideals in a commutative unital ring <math>A</math>, with the property that any two of them are ''...2008-03-15T22:30:51Z<p>New page: {{indispensable lemma}} ==Statement== Suppose <math>I_1, I_2, \ldots, I_n</math> are ideals in a <a href="/wiki/Commutative_unital_ring" title="Commutative unital ring">commutative unital ring</a> <math>A</math>, with the property that any two of them are ''...</p>
<p><b>New page</b></p><div>{{indispensable lemma}}<br />
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==Statement==<br />
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Suppose <math>I_1, I_2, \ldots, I_n</math> are ideals in a [[commutative unital ring]] <math>A</math>, with the property that any two of them are ''comaximal''; in other words, <math>I_r + I_s = A</math> for <math>r \ne s</math>. Then the natural map below is an isomorphism:<br />
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<math>A/(I_1I_2 \ldots I_n) \to A/I_1 \times A/I_2 \times \ldots A/I_n</math><br />
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The ''injectivity'' of this map translates to the statement:<br />
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<math>I_1I_2\ldots I_n = I_1 \cap I_2 \cap \ldots \cap I_n</math></div>Vipul