Ext and the square lemma.

Abstract

In his book "Lectures on Rings and Modules" Professor J. Lambek introduced Extl based on the "Square Lemma". In this thesis his approach has been used to define Extn for any positive integer n. This definition will be called symmetric definition of Ext n, since it is symmetric in both projective and injective modules. The equivalence of this new definition of Extn and the ordinary one has been shown. This symmetric definition together with the Square Lemma gives us an elegant method of diagram chasing, by squares instead of elements. Some applications are given.