Grobner bases and primary decomposition in polynomial rings in one variable over Dedekind domains

Let D be a Dedekind domain with quotient field K, let x be a single variable, and let I be an ideal in D [x]. In this paper we will describe explicitly the structure of a Grobner basis for I and we will use this Grobner basis to compute the primary decomposition of I. This Grobner basis also has a property similar to that of strong Grobner bases over PID's ([7], see also [1]). (C) 1997 Elsevier Science B.V.