The reciprocal complements of classes of integral domains

Given an integral domain D with quotient field Q ( D ) , the reciprocal complement of D is the subring R ( D ) of Q ( D ) whose elements are all the sums 1 d 1 + … + 1 d n for d 1 , … , d n nonzero elements of D . In this article we study problems related with prime ideals, localizations and Krull dimension of rings of the form R ( D ) and we describe the reciprocal complements of classes of domains, including semigroup algebras and D + m constructions. We also characterize when R ( D ) is a DVR.