a very simple presentation of the notion of universal property, with many examples; Sections 1.2 to 1.4 are devoted to this subject.
additional information about categories of modules; Sections 1.5 to 1.9 contain reminders about exact sequences, usual functors, projective modules and changes of basic rings; but in 1.8 finitely presented modules are treated with more detail.
a self-contained presentation of rings and modules of fractions, localization and globalization; although this material is already well treated in the existing literature, a concise exposition of the exact part that is here actually useful should prevent beginners from wandering in too-specialized topics.
KeywordsExact Sequence Prime Ideal Local Ring Maximal Ideal Direct Summand
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