Problem book on modules and algebras. (Q2881307)

This book contains a rich treasure of 333 problems, sorted into 8 chapters. The first 7 of these chapters deal with modules; only the last one contains exercises on Artin algebras. A full solution to each problem is provided, so the book as such is meant rather for the lecturer, than for the student. The problems in the book are on the level of 4th year mathematics students and will prove a handy companion to any faculty member teaching module theory on that level. It may also serve as a quick reference guide on results concerning a wide range of module theoretic material.NEWLINENEWLINE At the beginning of each chapter, a list of notations and sometimes a list of definitions is provided, together with references to textbooks containing more information on the topic. The most regular referenced books are those of \textit{R. Wisbauer}, [Foundations of module and ring theory. A handbook for study and research. Algebra, Logic and Applications 3. Philadelphia: Gordon and Breach Science Publishers (1991; Zbl 0746.16001)], \textit{M. Auslander, I. Reiten} and \textit{S. O. Smalø}, [Representation theory of Artin algebras. Cambridge Studies in Advanced Mathematics 36. Cambridge: Cambridge University Press (1995; Zbl 0834.16001)], and \textit{T. Albu}, [Lessons on the Grotendieck category \(\sigma[M]\). Bucureşti: Editura Universităţii (2004; Zbl 1258.16011)]. In many instances exercises lead to the definition of a concept, which is then stated.NEWLINENEWLINE The chapters in the problem book are: Chapter 1: Rings; Chapter 2: Modules; Chapter 3: Categories and Functors; Chapter 4: Generating, cogenerating and subgenerating modules; Chapter 5: Injective and Projective modules; Chapter 6: Semisimple modules; Chapter 7: Noetherian and Artinian modules, and Chapter 8: Artin algebras.