On Extension modules of finite homological dimension

Abstract: We explore the implications of the finiteness of homological dimensions for Ext modules, focusing on projective dimension, injective dimension, and their Gorenstein counterpart. In this direction, we establish several finiteness criteria for homological dimensions. Our results include the consequences of the finiteness of the Gorenstein (injective) dimension of the deficiency modules as well as a duality for certain Ext modules, all of finite (Gorenstein) projective dimension.