The w-integral closure of integral domains

Let D be an integral domain with quotient field K, the integral closure of D, X an indeterminate over D, and Nv={f∈D[X]|(Af)v=D}. Let w be the ∗-operation on D defined by , and let . Then Dw, called the w-integral closure of D, is an integrally closed overring of D. In this paper, we show that and . Using this result, we give several w-integral closure analogs of the integral closure. We also study the w-integral closure of UMT-domains and strong Mori domains.