ABSTRACT
In what follows, we fix the following notations unless otherwise specified: Let R denote a Noetherian domain, K denote its quotient field, and R[X ] denote a polynomial ring over R. Let η(X ) be an element in the quotient field K (X ) of R[X ] and put η(X ) = ψ(X )/φ(X ), where ψ(X ), φ(X ) ∈ K [X ] with (φ(X ), ψ(X ))K [X ] = K [X ] and φ(X ) monic. Note that expression η(X )/φ(X ) is unique. Let deg φ(X ) =: .
