# 2024-10-03

This following is a very brief summary of what happened in class on 2024-10-03.

We introduced three new constructions on modules:

1. The direct product of a pair of

2. The direct sum of a pair of

3. The sum of a pair of submodules of a given

We outlined the three constructions (as sets with operations and

Tomorrow we'll briefly outline some of the main properties of the three constructions, including when they're different (the default situation) and when they're the same/isomorphic (in some special situations). We'll then return to the general idea of "universal properties" and see if we can't firm things up a bit.

## Concepts

- Direct products of modules
- Direct sums of modules
- Sums of submodules
- Direct products vs. direct sums vs. sums

## References

- Dummit & Foote: Section 10.3