Lectures in General Algebra

A. G. Kurosh, I. N. Sneddon, M. Stark, S. Ulam

• Publisher: Pergamon
• Year: 2014
• Print ISBN: 9780080103525
• eBook ISBN: 9781483149578
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the convenience of constructing a single theory from the results of group experiments and ring experiments which are known to follow simple corollaries. The text also presents algebraic structures that are not of binary nature. From this parallelism arise other concepts, such as that of the lattices, complete lattices, and modular lattices. The book then proves the Schmidt-Ore theorem, and also describes linear algebra, as well as the Birkhoff-Witt theorem on Lie algebras. The text also addresses ordered groups, the Archimedean groups and rings, and Albert's theorem on normed algebras. This book can prove useful for algebra students and for professors of algebra and advanced mathematicians.

Table of contents

• Front Cover
• Lectures in General Algebra
• Copyright Page
• Table of Contents
• PREFACE
• CHAPTER ONE. RELATIONS
• CHAPTER TWO. GROUPS AND RINGS
• CHAPTER THREE. UNIVERSAL ALGEBRAS GROUPS WITH MULTI-OPERATORS
• CHAPTER FOUR. LATTICES
• CHAPTER FIVE. OPERATOR GROUPS AND RINGS. MODULES. LINEAR ALGEBRAS
• CHAPTER SIX. ORDERED AND TOPOLOGICAL GROUPS AND RINGS. NORMED RINGS
• BIBLIOGRAPHY
• INDEX
• OTHER TITLES IN THE SERIES IN PURE AND APPLIED MATHEMATICS