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.

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Yes, you can access Lectures in General Algebra by A. G. Kurosh, I. N. Sneddon,M. Stark,S. Ulam in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebra. We have over one million books available in our catalogue for you to explore.

Information

Publisher

Pergamon

Year

2014

ISBN

9781483149578

Topic

Mathematics

Subtopic

Algebra

Index

Mathematics

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