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<p>set. The ring structure for  consists of addition defined by  and multiplication defined by <br/>
* Although the ring  is a <a href="page.php?w=field_%28mathematics%29">field</a>,  is not because the nonzero element  does not have a <a href="page.php?w=multiplicative_inverse">multiplicative inverse</a>.</p>

<p>In a similar manner, the direct product of finitely many algebraic structures can be talked about; for example,  That relies on the direct product being <a href="page.php?w=associative">associative</a> <a href="page.php?w=up_to">up to</a> <a href="page.php?w=isomorphism">isomorphism</a>.</p><p>
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