I was wondering if there exists a nice overview for properties of modules like being cyclic, simple, semisimple, indecomposable, free, noetherian, artinian and having finite length. I'm thinking about some kind of diagram or table that shows which property implies which under certain conditions or provides counterexamples. Any help is welcome.
2026-04-29 12:14:24.1777464864
Overview for properties of modules
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The Database of Ring Theory has a section for modules now too. Unfortunately, I have not yet included dot graphs for the relationships between properties, but I generated one just for you here.
Don't take the chart as anything close to comprehensive: it's just starting out. There aren't any comprehensive resources, really.
As for examples and counterexamples, you can browse examples here and do searches here and so on.
There are more theorems used than is evident from this simple graph, but they are currently only accessible through the github repo.