2011/10/28 by Duong Quôc Việt, Viet, Duong Quoc, Van Dinh, Le +2
Computer Science · Mathematics · #13H15 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1110.6239
openalex publication_date 2011/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (A, \frak m) be a noetherian local ring with maximal ideal \frakm and infinite residue field k = A/\frakm. Let J be an \frak m-primary ideal, I1,...,Is ideals of A, and M a finitely generated A-module. In this paper, we interpret mixed multiplicities of (I1,..., Is,J) with respect to M as multiplicities of joint reductions of them. This generalizes the Rees's theorem on mixed multiplicity (Theorem 2.4). As an application we show that mixed multiplicities are also multiplicities of Rees's superficial sequences.