ON THE FINITENESS OF EXT-INDICES OF RING EXTENSIONS

The main goal of this paper is to investigate the finiteness of Ext-indices of ring extensions. We discuss some known related conjectures in the literature and observe the relationships among them within large classes of rings. This allows us to present interesting special cases verifying these conjectures. Finally, we tackle questions on the vanishing of Ext-index of trivial extensions of Artinian rings. We put the new results into use to construct new families of examples subject to the Gorenstein or Cohen-Macaulay conditions with finite Ext-index.