In a previous paper the last two authors introduced a condition which
gave an elementwise characterization of subintegrality for an extensio
n A subset of or equal to B of commutative Q-algebras. In the present
paper we show that the same condition gives an elementwise characteriz
ation of weak subintegrality for an extension A subset of or equal to
B of arbitrary commutative rings. We also give a new characterization
of weakly subintegral elements in which the ''coefficients'' lie in A
rather than B.