Ebook: Basic Structures of Modern Algebra

This book has developed from a series of lectures which were given by the author in mechanics-mathematics department of the Moscow State University. In 1981 the course "Additional chapters in algebra" replaced the course "Gen­ eral algebra" which was founded by A. G. Kurosh (1908-1971), professor and head of the department of higher algebra for a period of several decades. The material of this course formed the basis of A. G. Kurosh's well-known book "Lectures on general algebra" (Moscow,1962; 2-nd edition: Moscow, Nauka, 1973) and the book "General algebra. Lectures of 1969-1970. " (Moscow, Nauka, 1974). Another book based on the course, "Elements of general al­ gebra" (M. : Nauka, 1983) was published by L. A. Skorniakov, professor, now deceased, in the same department. It should be noted that A. G. Kurosh was not only the lecturer for the course "General algebra" but he was also the recognized leader of the scientific school of the same name. It is difficult to determine the limits of this school; however, the "Lectures . . . " of 1962 men­ tioned above contain some material which exceed these limits. Eventually this effect intensified: the lectures of the course were given by many well-known scientists, and some of them see themselves as "general algebraists". Each lecturer brought significant originality not only in presentation of the material but in the substance of the course. Therefore not all material which is now accepted as necessary for algebraic students fits within the scope of general algebra.

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This volume has developed from courses given at Moscow State University. The main purpose of the material presented is to introduce the concepts, results and problems of contemporary algebra, assuming some knowledge of the standard theory of linear algebra and vector spaces. One important aspect is also to demonstrate how the concepts discussed relate to each other and how they work in practice. The book begins with an introduction to the fundamental concepts of groups, rings, fields and modules and their representations. The seven chapters which follow are devoted respectively to the following topics: commutative algebra; groups; associative rings; Lie algebras; homological algebra; algebraic groups; and varieties of algebras. The volume concludes with a supplement dealing with set theory, references and indices.
The book is as self-contained as possible.
For graduate students and researchers wishing to obtain a good introduction to the concepts of contemporary algebra.

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This volume has developed from courses given at Moscow State University. The main purpose of the material presented is to introduce the concepts, results and problems of contemporary algebra, assuming some knowledge of the standard theory of linear algebra and vector spaces. One important aspect is also to demonstrate how the concepts discussed relate to each other and how they work in practice. The book begins with an introduction to the fundamental concepts of groups, rings, fields and modules and their representations. The seven chapters which follow are devoted respectively to the following topics: commutative algebra; groups; associative rings; Lie algebras; homological algebra; algebraic groups; and varieties of algebras. The volume concludes with a supplement dealing with set theory, references and indices.
The book is as self-contained as possible.
For graduate students and researchers wishing to obtain a good introduction to the concepts of contemporary algebra.

Content:
Front Matter....Pages i-ix
Introduction....Pages 1-49
Commutative Algebra....Pages 51-103
Groups....Pages 105-156
Associative Rings....Pages 157-198
Lie Algebras....Pages 199-243
Homological Algebra....Pages 245-287
Algebraic Groups....Pages 289-334
Varieties of Algebras....Pages 335-373
Set-Theoretic Supplement....Pages 375-395
Back Matter....Pages 397-422

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This volume has developed from courses given at Moscow State University. The main purpose of the material presented is to introduce the concepts, results and problems of contemporary algebra, assuming some knowledge of the standard theory of linear algebra and vector spaces. One important aspect is also to demonstrate how the concepts discussed relate to each other and how they work in practice. The book begins with an introduction to the fundamental concepts of groups, rings, fields and modules and their representations. The seven chapters which follow are devoted respectively to the following topics: commutative algebra; groups; associative rings; Lie algebras; homological algebra; algebraic groups; and varieties of algebras. The volume concludes with a supplement dealing with set theory, references and indices.
The book is as self-contained as possible.
For graduate students and researchers wishing to obtain a good introduction to the concepts of contemporary algebra.

Content:
Front Matter....Pages i-ix
Introduction....Pages 1-49
Commutative Algebra....Pages 51-103
Groups....Pages 105-156
Associative Rings....Pages 157-198
Lie Algebras....Pages 199-243
Homological Algebra....Pages 245-287
Algebraic Groups....Pages 289-334
Varieties of Algebras....Pages 335-373
Set-Theoretic Supplement....Pages 375-395
Back Matter....Pages 397-422
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