A note on joint reductions and mixed multiplicities

Duong Quoc Viet, Le Van Dinh, Truong Thi Hong Thanh
2014 Proceedings of the American Mathematical Society  
Let (A, m) be a noetherian local ring with maximal ideal m and infinite residue field k = A/m. Let J be an m-primary ideal, I 1 , . . . , I s ideals of A, and M a finitely generated A-module. In this paper, we interpret mixed multiplicities of (I 1 , . . . , I s , J) with respect to M as multiplicities of joint reductions of them. This generalizes Rees's theorem on mixed multiplicity. As an application we show that mixed multiplicities are also multiplicities of Rees superficial sequences.
doi:10.1090/s0002-9939-2014-11916-2 fatcat:bvq5fcsbl5cfppb7soizstd4b4