Foundations of module and ring theory: a handbook for study and research - v. 3 (Rev. and updated English ed.)

This volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work.

It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume.

Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs.

For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category.

Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings.

Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.