# Tag Archives: isomorphism theorems

## Elementary Module Theory (III): Approaching Linear Algebra

The Hom Group Continuing from the previous installation, here’s another way of writing the universal properties for direct sums and products. Let Hom(M, N) be the set of all module homomorphisms M → N; then: (*) for any R-module N. In the case where there’re finitely … Continue reading

## Elementary Module Theory (II)

Having defined submodules, let’s proceed to quotient modules. Unlike the case of groups and rings, any submodule can give a quotient module without any additional condition imposed. Definition. Let N be a submodule of M. By definition, it’s an additive … Continue reading

## Topology: More on Algebra and Topology

We’ve arrived at the domain where topology meets algebra. Thus we have to proceed carefully to ensure that the topology of our algebraic constructions are well-behaved. Let’s look at topological groups again. Our first task is to show that the … Continue reading