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.