This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module.

Bernard R. McDonald is Program Director for Algebra and Number Theory for the Division of Mathematical Sciences of the National Science Foundation, Washington D.C.

1. Matrix Theory Over Commutative Rings 2. Free Modules 3. The Endomorphism Ring of a Projective Module 4. Projective Modules 5. Theory of a Single Endomorphism