### On hereditary artinian rings and the pure semisimplicity conjecture: rigid tilting modules and a weak conjecture

José L. García (2014)

Colloquium Mathematicae

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A weak form of the pure semisimplicity conjecture is introduced and characterized through properties of matrices over division rings. The step from this weak conjecture to the full pure semisimplicity conjecture would be covered by proving that there do not exist counterexamples to the conjecture in a particular class of rings, which is also studied.