Let R be a domain with quotient field K and prime subring A. Then R is integral over each of its subrings having quotient field K if and only if (A,R) is a survival pair. This shows the redundancy of a condition involving going-down pairs in a earlier characterization of such rings. In characteristic 0, the domains being characterized are the rings R that are isomorphic to subrings of the ring of all algebraic integers. In positive (prime) characteristic, the domains R being characterized are of two kinds: either R = K is an algebraic field extension of A or precisely one valuation domain of K does not contain R.

Keywords: integral domain, survival pair, survival extension, lying-over, prime ideal, integral, subring, Krull dimension, ring of algebraic integers, characteristic.