Separative ideals of exchange rings. (Q553421)

The author studies necessary and sufficient conditions such that an ideal \(I\) of an exchange ring is separative. These conditions show that \(I\) is separative if and only if the ideal of the lower (upper) triangular matrices over \(I\) is also separative (Theorem 3.4). In the end of the paper it is shown that for regular rings this property can be described using comparability of modules (Theorem 4.5).