ABSTRACT
In Chapter 1 we examined the ring R regarded as a module over itself. We made an introductory survey of the summands, submodules, and factor modules of R. Through the use of the identity element of R, we encountered the concept of a projective module. The pattern of development of Chapter 1 and the concepts introduced there prove an introduction to the general theory of projectivity. The role played by the R-module R in Chapter 1 will now be taken over by the class of all coproducts of copies of the module R or, more generally, by the free left R-moduIes.
