Gröbner bases and primary decomposition in polynomial rings in one variable over Dedekind domains Original Research Article

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 Gröbner basis for I and we will use this Gröbner basis to compute the primary decomposition of I. This Gröbner basis also has a property similar to that of strong Gröbner bases over PIDʹs ([7], see also [1]).