Topics in torsion theory

The purpose of this thesis is to generalize to the torsion-theoretic setting various concepts and results from the theory of rings and modules. In order to accomplish this we begin with some preliminaries which introduce the main ideas used in torsion theory, the major ones being r-torsion and r-torsionfree modules as well as r-dense and r-pure submodules. In the first chapter we also introduce a new concept, that of a r-compact module, which is basic enough to deserve a place among the preliminaries.