Basic Abstract Algebra

This book is intended as a text on abstract algebra for undergraduate students and is divided into five parts. The first part contains an informal introduction to sets, number systems, matrices, and determinants. The second part deals with groups, the third part treats rings and modules, the fourth is concerned with field theory. Much of the material in Parts II, III, IV forms the core syllabus of a course in abstract algebra. The fifth part goes on to.treat some additional optional topics often taught to undergraduates. This book presents a complete course in abstract algebra, giving lecturers flexibility in the selection of topics to be taught in individual classes. Complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. In addition, the book contains many examples fully worked out and a variety of problems for practice and challenge. Solutions to the odd-numbered problems are provided at the end of the book to encourage the student in problem solving.