Induced liftings, exchange rings and semi-perfect algebras. (Q979053)

Several important classes of rings can be characterized in terms of liftings of idempotents with respect to various ideals; classical examples are semi-perfect rings, semi-regular rings and exchange rings. In this paper the author begins with a study of some extensions of the concept of idempotent lifting and proves generalizations of some classical theorems. Then the author describes the method of induced liftings, which allows us to transfer liftings from a ring to its subrings. Using this method we are able to show that under certain assumptions a subring of an exchange ring is also an exchange ring, and to prove that a finite algebra over a commutative local ring is semi-perfect, provided it can be suitably represented in an exchange ring.