Annihilation of cohomology and strong generation of module categories (Q2797800)

The authors introduce the cohomology annihilator of a noetherian ring \(\Lambda\) which is a finitely generated module over its center. They also say that a right \(\Lambda\)-module \(G\) is a strong generator for the category of finitely generated right \(\Lambda\)-modules if it contains \(\Lambda\) as a direct summand and there exist integers \(s\) and \(n\) such that for any right \(\Lambda\)-module \(M\), there is a \(\Lambda\)-module \(M\) and a filtration \(0=Z_0\subseteq Z_1\subseteq \ldots \subseteq Z_n=Z\), where \(Z=W\oplus \Omega^sM\), with \(Z_{i+1}/Z_i\) in \(\mathrm{add} G\) for each \(i\); here \(\Omega^sM\) denotes the \(s\)th syzygy module of \(M\). Several results connecting the existence of non-trivial cohomology annihilators and the existence of strong generators for the category of finitely generated modules. Several results about cohomology annihilators of commutative rings and strong finite generation of the corresponding bounded derived category are extended.