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Book review

Author(s) Bahturin, Y.
Title Basic structures of modern algebra
Publisher Kluwer Academic Publishers
Year of publication 1993
Reviewed by Andrei Marcus

This book is written by a very well known researcher and expositor. Its content is based on the series of lectures given by the author at Moscow State University in the last decade.

The author's intention is to introduce the important concepts, results and problems of contemporary algebra in a highly self contained material, which actually assumes only the knowledge of the first year linear algebra, since it includes an introduction on Groups, Rings and Modules. I shall enumerate the chapters of the volume: 1. Commutative algebra; 2. Groups; 3. Associative rings; 4. Lie algebras; 5. Homological algebra; 6. Algebraic groups; 7. Varieties of algebras.

In spite of this variety of subjects, the author manages to present in a very comprehensive and attractive way many deep results and fundamental ideas, and also the links between these topics are very well underlined. There are no exercises, but many examples illustrate the theory. The book ends with a set-theoretic supplement, references (which are in the same time recommendations for further reading) and good index.

This volume is an excellent reading for students after the first two year general algebra courses. University lecturers may also find here suggestions for their teaching.