<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- -->
<!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html -->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" >
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head><title>associated primes of an ideal</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_primary_spdecomposition.html">next</a> | <a href="_minimal_spprimes_spof_span_spideal.html">previous</a> | <a href="_primary_spdecomposition.html">forward</a> | <a href="_minimal_spprimes_spof_span_spideal.html">backward</a> | <a href="_ideals.html">up</a> | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div>
</td>
</tr>
</table>
<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_ideals.html" title="">ideals</a> > <a href="_associated_spprimes_spof_span_spideal.html" title="">associated primes of an ideal</a></div>
<hr/>
<div><h1>associated primes of an ideal</h1>
<div>The function <a href="_associated__Primes.html" title="find the associated primes of an ideal">associatedPrimes</a> returns a list of the associated prime ideals for a given ideal I. The associated prime ideals correspond to the irreducible components of the variety associated to <tt>I</tt>. They are useful in many applications in commutative algebra, algebraic geometry and combinatorics.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a..d];</pre>
</td></tr>
<tr><td><pre>i2 : I = ideal(a*b-c*d, (a*c-b*d)^2);
o2 : Ideal of R</pre>
</td></tr>
<tr><td><pre>i3 : associatedPrimes I
o3 = {ideal (d, a), ideal (b + c, a + d), ideal (c, b), ideal (b - c, a - d)}
o3 : List</pre>
</td></tr>
</table>
See <a href="_primary_spdecomposition.html" title="">primary decomposition</a> for more information about finding primary decompositions. To find just the minimal prime ideals see <a href="_minimal_spprimes_spof_span_spideal.html" title="">minimal primes of an ideal</a>.</div>
</div>
</body>
</html>
