Strong Prüfer rings and the ring of finite fractions (Q1208218)

Let \(R\) be a commutative ring with identity, \(T(R)\) its total quotient ring, and \(Q(R)\) its complete ring of quotients. Denote by \(Q_ 0(R)\) the ring of finite fractions of \(R\), which is a subring of \(Q(R)\) containing \(T(R)\). The author defines a \(Q_ 0\)-Prüfer ring as a ring \(R\) for which every ring between \(R\) and \(Q_ 0(R)\) is integrally closed in \(Q_ 0(R)\). It is shown that every strong Prüfer ring is a \(Q_ 0\)-Prüfer ring and every \(Q_ 0\)-Prüfer ring is a Prüfer ring, and the above inclusions between these classes of rings are strict. It is also proved that \(R\) is a strong Prüfer ring if and only if \(R\) is a \(Q_ 0\)-Prüfer ring with \(Q_ 0(R)\) having a certain property called by the author ``property A''.