Attached primes of local cohomology modules and structure of Noetherian local rings

Let (R,m)(R,m) be a Noetherian local ring and M a finitely generated R  -module. It is well known that the local cohomology module Hmi(M) is Artinian for all i⩾0i⩾0. Following I.G. Macdonald [8], denote by AttRHmi(M) the set of attached primes of Hmi(M). This paper is concerned with clarifying the structure of the base ring R   via a relation between AttRHmi(M) and AttRˆHmi(M). Some characterizations for R being universally catenary with all Cohen–Macaulay formal fibers are given.