ABSTRACT ALGEBRA

This book on algebraic systems is designed to be used either as a supplement to current texts or as a stand-alone text for a course in modern abstract algebra at the junior and senior levels. In addition, graduate students can use this book as a source for review. As such, this book is intended to provide a solid foundation for future study of a variety of systems rather than to be a study in depth of any one or more. The basic ingredients of algebraic systems¿sets of elements, relations, operations, and mappings¿are discussed in the ¿rst two chapters. The format established for this book is as follows: a simple and concise presentation of each topic.a wide variety of familiar examples. proofs of most theorems included among the solved problemsa carefully selected set of supplementary exercises. In this upgrade, the text has made an e¿ort to use standard notations for the set of natural numbers, the set of integers, the set of rational numbers, and the set of real numbers. In addition, de¿nitions are highlighted rather than being embedded in the prose of the text.