Abstract
A hereditary torsion theory is simple if it is generated by a class of simple modules. There is a fairly large class of rings, including e.g. the artinian rings, for which all hereditary torsion theories are simple. Therefore it is of a certain interest to study simple torsion theories in some detail. The methods to be used for that purpose are the basic ones of the theory of artinian rings, such as the use of the Jacobson radical and the lifting of idempotents. This chapter is devoted to the development of these methods and to their applications to torsion theory, as well as to an account of the basic theory of rings with various minimum conditions.
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