# Tag Archives: modules

## 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\\ […]

## The Double Dual and Morita Duality

Here is a fact from linear algebra: if $V$ is a finite dimensional vector space over a field $k$ then $V$ is naturally isomorphic to its double dual. Of course, it is also isomorphic to its dual as well, but it is the natural isomorphism that is more interesting. Write \$ V^* […]