Groups & Rings

Abstract algebra provides many foundations for other branches of mathematics. This book, based upon over a decade of independent study outside the classroom, is a detailed and thorough introduction to the subject. The work begins with a review of preliminary definitions and facts of sets, relations and maps, and then leads the reader through the study of groups, rings and fields. Unlike other books on the subject, this book includes the important implications and constraints which result from total order relations on these structures. Throughout this development, the topics are presented with an emphasis on theory over application. The reader is assumed to have no previous knowledge of abstract algebra, although some experience with logic as used in mathematical proofs such as induction and contraposition will be helpful. The book is not intended as a textbook and is suitable for someone pursuing the study of abstract algebra as a hobby outside the classroom.