Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Abstract:
For finitely generated modules over a Noetherian ring , we study the following properties about primary decomposition: (1) The Compatibility property, which says that if and is a -primary component of for each , then ; (2) For a given subset , is an open subset of if and only if the intersections for all possible -primary components and of ; (3) A new proof of the `Linear Growth' property, which says that for any fixed ideals of there exists a such that for any there exists a primary decomposition of such that every -primary component of that primary decomposition contains .