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Book review

Author(s) Bahturin, Yuri
Title Basic Structures of Modern Algebra
Publisher Kluwer Academic Publishers
Year of publication 1993
Reviewed by Vasile Postolica

The main goal of this book, based on the series of lectures given by the autor in the Mechanics-Mathematics Department of Moscow State University, is to introduce the beginners to the concepts, results, and problems of contemporary algebra, starting from the standard theory of linear algebra and vector spaces. At the same time the author gives emphasis to the main connections between various concepts. Thus, after a short Preface followed by some recommendations for the reader, in Introduction the author explains the main definitions and results in group, ring, and field theory. Chapter 1 is devoted to commutative algebra. The groups are discussed in Chapter 2. Chapter 3 deals with associative rings and the Lie algebras are considered in Chapter 4. The subject of Chapter 5 is homological algebra. The algebraic groups are presented in Chapter 6. The last chapter of the book is devoted to varieties of algebras. The book also contains a Set-theoretic supplement, selected references, a symbol index, and a subject index. This textbook is written clearly, with significant comments, examples, and proofs. For this reason this book is a genuine and recent introducition in the fascinating field of classical algebra.