On the unmixedness and universal catenaricity of local rings and local cohomology modules

Let (R,m) be a Noetherian local ring and M a finitely generated R-module. Let i⩾0 be an integer. Consider the following property for the Artinian local cohomology module Hmi(M)(∗)AnnR(0:Hmi(M)p)=pfor all p∈Var(AnnR(Hmi(M))). In this paper, we study the property (∗) of Hmi(M) in order to investigate the universal catenaricity of the ring R/AnnRM and the unmixedness of the ring R/p for certain p in SuppM. We also characterize the property (∗) for Hmi(M) and obtain the associativity formulae for multiplicity of Hmi(M) in case where Hmi(M) satisfies the property (∗).