Abstract
Let A be a Koszul algebra and M a finitely generated graded A-module. Suppose that M is generated in degree 0 and has a pure resolution. We prove that, if rℰ(M) ≠ 0 then M is Koszul; and if in addition M is not projective, then the converse is true as well, where r denotes the graded Jacobson radical of the Yoneda algebra [Formula: see text] of A, and [Formula: see text] denotes the Ext module of M.
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