Abstract

This paper is concerned with a finitely generated module over a(commutative Noetherian) local ring . In the case when is a homomorphic image of a Gorenstein local ring, one can use the well-known associativity formula for multiplicities, together with local duality and Matlis duality, to produce analogous associativity formulae for the local cohomology modules of with respect to the maximal ideal. The main purpose of this paper is to show that these formulae also hold in the case when is universally catenary and such that all its formal fibres are Cohen-Macaulay. These formulae involve certain subsets of the spectrum of called the pseudo-supports of ; these pseudo-supports are closed in the Zariski topology when is universally catenary and has the property that all its formal fibres are Cohen-Macaulay. However, examples are provided to show that, in general, these pseudo-supports need not be closed. We are able to conclude that the above-mentioned associativity formulae for local cohomology modules do not hold over all local rings.