EXTENSIONS R[α] ∩ R[α?1] AND R[α ? a] ∩ R[(α ? a)?1] OF A NOETHERIAN DOMAIN R

Let R be a Noetherian domain and α an anti-integral element of degree d over R. Let a and b be elements of R. In this paper, we give a condition for R(α ? a)^?1] to be coincide with R(α ? b)^?1]. Moreover, we give a sufficient condition for Rα] ∩ Rα^?1] to be Rα ? a] ∩ R(α ? a)^?1].