The reciprocal complement of a polynomial ring in several variables over a field

The *reciprocal complement* $R(D)$ of an integral domain D is the subring of its fraction field generated by the reciprocals of its nonzero elements. Many properties of $R(D)$ are determined when D is a polynomial ring in n≥ 2 variables over a field. In particular, $R(D)$ is an n-dimensional, local, non-Noetherian, non-integrally closed, non-factorial, atomic G-domain, with infinitely many prime ideals at each height other than $0$ and n.