Extensions R[α − a] ∩ R[(α − a)− 1] with an Anti-integral Element α Are Unchanged for Any a R

Let R be an integral domain and α an anti-integral element of degree d over R. It is shown that the equality R[α − a] ∩ R[(α − a)− 1] = R[α] ∩ R[α− 1] holds for any a R with α − a ≠ 0.