Modules with Pure Resolutions over Koszul Algebras Revisited
I construct a Koszul algebra A and a finitely generated graded A-module M that together form a counterexample to a recently published claim. M is generated in degree 0 and has a pure resolution, and the graded Jacobson radical of the Yoneda algebra of A does not annihilate the Ext module of M, but nonetheless M is not a Koszul module.
Journal of Algebra and Its Applications
Cassidy, Thomas. "Modules with Pure Resolutions over Koszul Algebras Revisited." Journal of Algebra and Its Applications (2016) : 50035-50035.