New homological invariants for modules over local rings, I Original Research Article

Auslanderʹs delta invariant over Gorenstein commutative local rings is generalized to arbitrary local rings via Vogelʹs construction of Tate (co)homology and a vanishing theorem is proved. Based on one of the new invariants, Auslanderʹs index of a Gorenstein local ring is generalized to arbitrary local rings and the finiteness of the new index is established.