Hilbert-Samuel Multiplicity and Northcott's Inequality Relative to an Artinian Module

Let (A, 𝔪) be a commutative quasi-local ring (with identity 1≠0), and let I ⊂ 𝔪 be an A-ideal such that l(0 :MI) < ∞. For M an Artinian A-module of N-dimension d, we introduce the notion of Hilbert...