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<a accesskey="3" href="page.php?w=associated_graded_ring&amp;p=2">3.Next</a>
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<p>In <a href="page.php?w=mathematics">mathematics</a>, the <b>associated graded ring</b> of a <a href="page.php?w=ring_%28mathematics%29">ring</a> R with respect to a proper <a href="page.php?w=ideal_%28ring_theory%29">ideal</a> I is the <a href="page.php?w=graded_ring">graded ring</a>:<br/>
:.Similarly, if M is a left R-module, then the <b>associated graded module</b> is the <a href="page.php?w=graded_ring">graded module</a> over :<br/>
:.</p>

<p><big> Basic definitions and properties </big></p>
<p>For a ring R and ideal I, multiplication in  is defined</p><p>
<a accesskey="3" href="page.php?w=associated_graded_ring&amp;p=2">3.Next</a>
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