https://commalg.subwiki.org/w/index.php?action=history&feed=atom&title=Symbolic_power_of_a_prime_idealSymbolic power of a prime ideal - Revision history2026-09-04T09:53:05ZRevision history for this page on the wikiMediaWiki 1.41.2https://commalg.subwiki.org/w/index.php?title=Symbolic_power_of_a_prime_ideal&diff=1274&oldid=prevVipul: 1 revision2008-05-12T16:34:59Z<p>1 revision</p>
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</td></tr></table>Vipulhttps://commalg.subwiki.org/w/index.php?title=Symbolic_power_of_a_prime_ideal&diff=1273&oldid=prevVipul at 07:40, 9 August 20072007-08-09T07:40:47Z<p></p>
<p><b>New page</b></p><div>==Definition==<br />
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Let <math>R</math> be a [[commutative unital ring]], <math>Q</math> a [[prime ideal]] of <math>R</math> and <math>n</math> a positive integer. The <math>n^{th}</math> symbolic power of <math>Q</math>, denoted as <math>Q^{(n)}</math> is defined as the set:<br />
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<math>\{ r \in R | sr \in Q^n, s \in R \setminus Q \}</math><br />
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Equivalently, it is the pre-image of the <math>n^{th}</math> power of the localized ideal <math>Q_Q</math> in the [[localization at a prime ideal|localization]] <math>R_Q</math>.</div>Vipul