Commutative Monoids, Noncommutative Rings and Modules

Abstract

These are the notes of a non-standard course of Algebra. It deals with elementary theory of commutative monoids and non-commutative rings. Most of what is taught in a master course of Commutative Algebra holds not only for com- mutative rings, but more generally for any commutative monoid, which shows that the additive group structure on a commutative ring has little importance.

In the rest of the notes of the course presented here, we introduce the basic no- tions of non-commutative rings and their modules, stressing the difference with what happens in the case of commutative rings.