The depth, the delooping level and the finitistic dimension

We investigate two invariants of Noetherian semiperfect rings, namely the depth and a new invariant we call “delooping level”. These give lower upper bounds for finitistic dimension, respectively. As first theorems, necessary sufficient criterion delooping level to be finite in terms splitting unit map related adjunction, use this torsionfreeness finiteness. further relate these Auslander–Bridger grade conditions modules, which are vanishing on double Ext duals. main theorem, prove that agree whenever non-trivial satisfied simple so either computes dimension case. Over Artinian show also big obtain cohomological conjecture hold. commutative local always hold characterisation as ring.