ABSTRACT
In this chapter we will expand our attention from the class of free modules to the class of all direct summands of free modules. Our goal is to develop as much insight into the structure of these modules as possible. Only the first steps can be taken in this chapter. We will give a survey discussion of this problem after making an observation that will allow us to shorten the phrase “a module isomorphic to a direct summand of a free module” to a single familiar word.
OBSERVATION 1. A left R-module is isomorphic to a direct summand of a free module if and only if it is projective.
