A Brief for Commutative Ring Theorists

In this chapterwe recapitulate some key results from Parts I and II whose formulations become notably simpler in the setting of commutativeNoetherian rings.Aconvention introduced in Chap. 1, namely that modules over a commutative ring tacitly are considered to be symmetric bimodules, now becomes crucial. The convention is both standard and useful, and not to adopt it might as a matter of fact be outright confusing: As we do not distinguish between a commutative ring and its opposite ring, there would be a clash with the conventions that all modules are left modules.