This question already has an answer here:
- Why are Noetherian Rings important? 4 answers
While in undergraduate years, abstract stuctures are very confusing since they arise without many motivations most of the times, and find their living ground later on. I would like to understand why noetherian rings are interesting.
Principal and euclidean rings are definitely useful to have arithmetic tools and notion generalizing those of the arithmetics of integers. What about noetherian rings? It often appears in arithmetic courses, however what allows them to do that other rings do not? What are the lost properties compared to a principal ring?
In one sentence: how to grasp the meaning and interest of noetherian rings (or other structures)?