I am preparing a write-up on Topics on Artinian Rings and Modules for a project. I hope to mention some unsolved problems in the domain of these objects along the way. Till now, I have been able to find and understand the statement of the Monomial Conjecture. Upon googling, I did not find problems that would serve my need as they were well over my head.

**Question**: Are there more well-known and simply-stated problems?

**P.S.**: By simply-stated, I mean understandable by a student comfortable with some theory of modules and rings, chain conditions on rings and modules, radicals(nil and Jacobson's), Nakayama's lemma and the Krull dimension of a ring plus some special topics. You can assume this to be my 'bailiwick' while suggesting problems.

Your assistance is greatly appreciated.