Primary decomposition of divisorial ideals in Mori domains (Q1121946)

A Mori domain is an integral domain which satisfies the ascending chain condition on divisorial ideals. In general, a divisorial ideal in a Mori domain is neither a finite intersection of divisorial primary ideals nor a finite intersection of primary ideals in the usual sense. The notion of divisorial irreducibility for divisorial ideals is introduced and studied. Necessary and sufficient conditions for the existence of divisorial primary decompositions are given. Some special techniques are used to show that every divisorial ideal of a two dimensional Mori domain has a primary decomposition.