New Invariants of Noetherian Local Rings

We investigate properties of certain invariants of Noetherian local rings, including their behavior under flat local homomorphisms. We show that these invariants are bounded by the multiplicity for Cohen–Macaulay local rings with infinite residue fields, and they all agree with the multiplicity when such rings are hypersurfaces. We also show that these invariants are all equal to 2 for a non-regular Cohen–Macaulay local ring A if and only if A has a minimal multiplicity, provided its residue field is infinite.