most recent 30 from http://mathoverflow.net 2013-05-24T22:24:35Z http://mathoverflow.net/feeds/question/31463 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/31463/how-much-can-we-say-about-the-number-of-nilpotents-in-a-finite-local-commutative Oliver 2010-07-11T20:57:31Z 2010-07-25T05:29:32Z

<p>A commutative ring is local if it has a single maximal ideal. If the ring is finite, this implies that all elements are either units or nilpotents. Further, all finite local rings have prime power order.</p> <p>Given a prime power $p^k$ and a positive integer $n &lt; p^k$, under what conditions on $p, k, n$ does there exist a local ring $R$ with $|R| = p^k$ and $n$ nilpotents?</p>