Noetherianity and Ext

E.L. Green, N. Snashall, Ø. Solberg, D. Zacharia
2008 Journal of Pure and Applied Algebra  
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 n R (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.
doi:10.1016/j.jpaa.2007.10.011 fatcat:k6r6gitxm5bexjgkl3qagbm3wu