On weak subintegrality
In a previous paper the last two authors introduced a condition which gave an elementwise characterization of subintegrality for an extension A ⊆ B of commutative ℚ-algebras. In the present paper we show that the same condition gives an elementwise characterization of weak subintegrality for an extension A ⊆ 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.
Reid, Les, Leslie G. Roberts, and Balwant Singh. "On weak subintegrality." Journal of Pure and Applied Algebra 114, no. 1 (1996): 93-109.
Journal of Pure and Applied Algebra