# Tag Archives: purity

## Pure exact sequences

Over the next few posts, I'll talk more about axiomatizability of algebraic structures in first-order logic. Before I do that, we need to know about purity of exact sequences. So let's fix a ring $R$. An exact sequence $$0\to A\to B\to C\to 0$$ in the category of left $R$ modules is called pure if for […]