From the MR review: "In this expository paper the authors give short, direct and elementary proofs (without using spectral sequences) for results on multiplicities due to Auslander-Buchsbaum, Boda-Vogel, Northcott, and Serre" and "for the basic properties of Serre's intersection multiplicities of embedded algebraic varieties along a simple proper component of their intersection." MR843111 (87m:13037)