Commutative quasiregular rings with isomorphic additive and circle composition groups, II: rational algebras

We show that any commutative nil ring which is an algebra over the rationals has its additive group isomorphic to its circle composition (or adjoint) group and demonstrate the importance of divisibility in establishing this result. We conclude by showing that if a ring has isomorphic additive and circle composition groups then this property need not be inherited by its quasiregular subrings. Copyright © 1998 by Marcel Dekker, Inc.