ABSTRACT
It is known that if α is a nonzero element in the quotient field K of an integral domain R, then R〈α〉 := R[α] ∩ R[α−1] is integral over R (cf. [K, Ex.4, page 12]). The ring R〈α〉 seems rather interesting to us, but we do not recall seeing any other results in the literature about such rings except in a few (e.g., [MR]).
