A generalization of Noetherian rings. (Q934296)

A ring \(R\) is left AFG if left annihilators of nonempty subsets \(X\subset R\) are finitely generated. In this clearly written article the author gives various equivalent characterizations of left AFG-rings. As a sample he proves that being left AFG is equivalent to cyclic right modules having projective preenvelopes. He gives an example showing that the property AFG is not left-right symmetric but then shows that there are properties of the ring that guarantee this symmetry. The article ends with various applications of the results concerning the AFG property.