Abstract

An effective way to understand the behavior of a ring R is to study the various ways in which R acts on its left and right modules. Thus, the theory of modules can be expected to be an essential chapter in the theory of rings. Classically, modules were used in the study of representation theory (see Chapter 3 in First Course). With the advent of homological methods in the 1950s, the theory of modules has become much broader in scope. Nowadays, this theory is often pursued as an end in itself. Quite a few books have been written on the theory of modules alone.KeywordsCommutative RingProjective ModuleFree ModuleDivision RingInjective ModuleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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