SEPARATIVE CANCELLATION FOR PROJECTIVE-MODULES OVER EXCHANGE RINGS

A separative ring is one whose finitely generated projective modules s atisfy the property A+A congruent to A+B congruent to B+B-->A congruen t to B. This condition is shown to provide a key to a number of outsta nding cancellation problems for finitely generated projective modules over exchange rings. It is shown that the class of separative exchange rings is very broad, and, notably, closed under extensions of ideals by factor rings. That is, if an exchange ring R has an ideal I with I and R/I both separative, then R is separative.