2025-11-07

This following is a very brief summary of what happened in class on 2025-11-07.

After recapping the general strategy, we spent the entire class working through the first half of the proof of the structure theorem for modules over a PID. Be sure to glance at the notes online for the full details.

Next class we'll complete the proof and see the important corollary, namely the fundamental theorem for modules over a PID.

Concepts

• Noetherian modules
• Linear independence, rank and the structure of free modules

References

• Dummit & Foote, Abstract Algebra: Section 12.1