Web Reference: Modules are a generalization of the vector spaces of linear algebra in which the \scalars" are allowed to be from an arbitrary ring, rather than a ̄eld. This rather modest weakening of the axioms is quite far reaching, including, for example, the theory of rings and ideals and the theory of abelian groups as special cases. (1.1) De ̄nition. “Module” will always mean left module unless stated otherwise. Most of the time, there is no reason to switch the scalars from one side to the other (especially if the underlying ring is commutative). A. Module 1 Summary of Changes (02/07/2014, version 2.3).........................................................39 B. Module 1 Summary of Changes (08/23/2013, version 2.2 ...
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