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

Abstract

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 $n\ge 2$ 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 $n$.

26 pages. Refereed version. We expanded the introduction, included additional explanations throughout, and changed the organization and theorem naming to better reflect the structure and aims of the work