Suppose that \(R\) is a commutative ring with unity, and \(N\subseteq M\) are \(R\)-modules. If \(\operatorname {Ext}^1(M/N,N)=0\), prove that the inclusion \(N\hookrightarrow M\) is split.
Question
Math 6310 • Algebra
Spring 2019 • Question 9
Question
Spring 2019 • Question 9
Suppose that \(R\) is a commutative ring with unity, and \(N\subseteq M\) are \(R\)-modules. If \(\operatorname {Ext}^1(M/N,N)=0\), prove that the inclusion \(N\hookrightarrow M\) is split.