most recent 30 from http://mathoverflow.net 2013-05-22T08:49:16Z http://mathoverflow.net/feeds/user/7729 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/32415/maximal-ideal-that-annihilates-entire-ring Edward Poon 2010-07-18T22:09:42Z 2010-11-04T23:52:43Z

<p>Does there exist a ring R with a nonzero maximal ideal M such that R^2=R and MR = RM = 0?</p> <p>Here R is associative but does not have an identity (obviously). It seems a simple enough question but I'm not even sure of the answer if I insist that M be the only proper ideal. I know R can't be commutative and that the conditions can't be relaxed (much); for example, there is a commutative ring satisfying these conditions if M need not be maximal.</p>