Abstract
Let R = R 0 ⊕ R 1 ⊕ R 2 ⊕ ⋯ be a graded algebra over a field K such that R 0 is a finite product of copies of K and each R i is finite dimensional over K . Set J = R 1 ⊕ R 2 ⊕ ⋯ and S = ⊕ n ≥ 0 Ext R n ( R / J , R / J ) . We study the properties of the categories of graded R -modules and S -modules that relate to the noetherianity of R . We pay particular attention to the case when R is a Koszul algebra and S is the Koszul dual to R .
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