QUASIREGULAR TORSION RINGS HAVING ISOMORPHIC ADDITIVE AND CIRCLE COMPOSITION GROUPS

Abstract

We investigate the role played by torsion properties in determining whether or not a commutative quasiregular ring has its additive and circle composition (or adjoint) groups isomorphic. We clarify and extend some results for nil rings, showing, in particular, that an arbitrary torsion nil ring has the isomorphic groups property if and only if the components from its primary decomposition into p-rings do too.