In this post, I'm going to write down the detailed proofs of some of the exercises in Rotman's Homological Algebra. They were asked in ML and then answered by me. 1. Let $latex A$ be a torsion abelian group. Then $latex \text{Ext}^1_\mathbb{Z}(A, \mathbb{Z}) \cong \text{Hom}_\mathbb{Z}(A,S^1)$, where $latex S^1$ is the unit circle. One point is … Continue reading Some Homological Algebra Computations