Towards a theory of R-modules modulo a Serre category

Abstract

This note is a brief excursion into a new theory of modules over a commutative ring R modulo a Serre subcategory S of the category of R-modules, in the sense that the modules of S are regarded as trivial. As a demonstration of the theory we have chosen to extend the primary decomposition theorem for submodules of a Noetherian .R-module from the familiar case of S trivial (i.e. the only R-module of S is the zero module) to the general case.