# 2024-09-26

This following is a very brief summary of what happened in class on 2024-09-26.

We defined module morphisms between left

: In this case, -modules are abelian groups and morphisms of such modules are simply group morphisms. , a field: In this case, -modules are -vector spaces and morphisms of such modules are -linear transformations. , where is a field: In this case, -modules are -vector spaces equipped with an -linear endomorphism (which encodes how acts on ). For such modules, morphisms correspond to -linear transformations "compatible with" the given -linear endomorphisms.

We also noted that for every ring **zero module** and denoted

## Concepts

## References

- Dummit & Foote: Section 10.2