# Tag Archives: diagram chasing

## The "Fractional" Isomorphism Theorem

For modules one has the isomorphism theorem $(A/C)/(B/C) \cong A/B$ for $C\leq B\leq A$. One way to remember it is through analogy with canceling of fractions. Another way to remember and prove it is to put all the modules in a 3×3 commutative diagram  \begin{matrix} C & \to & B & \to & B/C\\ […]

## Wild Spectral Sequences Ep. 4: Schanuel's Lemma

It's time for another installment of Wild Spectral Sequences! We shall start our investigations with a classic theorem useful in many applications of homological algebra called Schanuel's lemma, named after Stephen Hoel Schanuel who first proved it. Consider for a ring $R$ the category of left $R$-modules, and let $A$ be any […]