Modules and homological algebra

Abstract

Homological algebra is a branch of mathematics that studies algebraic structures through their associated chain complexes and homology groups. It has its origins in algebraic topology, but has since been applied to other areas of mathematics such as algebraic geometry and repre- sentation theory. This thesis provides a brief introduction into the theory required for the basic theory of homological algebra, where the Tor and the Ext will be studied. Some characteriza- tions between projective modules, Tor and Ext were made. The Tor was also balanced, which allows for Tor group calculations to be made much easier in the future.