Making an algebra the uniqe maximal one-sided ideal in another unital algebra - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T21:33:36Z http://mathoverflow.net/feeds/question/95285 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/95285/making-an-algebra-the-uniqe-maximal-one-sided-ideal-in-another-unital-algebra Making an algebra the uniqe maximal one-sided ideal in another unital algebra princehall 2012-04-26T18:40:18Z 2012-04-26T21:19:48Z <p>If $R$ is an algebra without a unit, then the standard unitisation $R^\sharp$ can have maximal one-sided ideals other than $R$. Thus, it is natural to ask about the following. Let $R$ be an algebra without a unit (over a field with char 0 if it does matter).</p> <p>Is there a unital algebra $A$ such that $R$ is the unique maximal right ideal in $A$?</p> <p>EDIT: Assume $R$ has a faithful representation $\pi$ on a vector space $V$ (over $K$), what if we consider $A=\pi(R)+KI$? </p>