User vova - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T17:01:46Z http://mathoverflow.net/feeds/user/24888 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/101294/extension-of-projective-module Extension of projective module vova 2012-07-04T08:31:30Z 2012-07-04T11:01:16Z <p>Hi all!</p> <p>I am interested in the following question in homological algebra.</p> <p>Let we have two noncommutative rings with homomorphism $\phi:B\rightarrow A$ and $M$ be a projective $A$-module. Consider the following extension of $M$ over $B$ </p> <p>$0\rightarrow M\rightarrow N\rightarrow M\rightarrow0$</p> <p>What is the obstruction for $N$ to be a projective $B$-module?</p> <p>In other words, which elements from $\text{Ext}^{1}_{B}(M,M)$ correspond to projective modules?</p>