Rational extensions of modules

Abstract

It is shown, that a module B is a rational extension of a submodule A if and only if B/A is a torsion module with respect to the largest torsion theory for which B is torsionfree. The rational completion of a module can thus be viewed as a module of quotients. The behavior of rationally complete modules under the formation of direct sums and products is studied. It is also shown, that a module is rationally complete provided it contains a copy of every nonprojective simple module.