On locally quasi A∗ algebras in codimension-one over a Noetherian normal domain

Let R be Noetherian normal domain. We shall call an R-algebra A quasi A∗ if A=R[X,(aX+b)−1] where X∈A is a transcendental element over R, a∈R∖0, b∈R and (a,b)R=R. In this paper we shall describe a general structure for any faithfully flat R-algebra A which is locally quasi A∗ in codimension-one over R. We shall also investigate minimal sufficient conditions for such an algebra to be finitely generated.