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.