A Course In Universal Algebra

The Millennium Edition Stanley Burris H. P. Sankappanavar A Course in Universal Algebra With 36 Illustrations c S. Burris and H.P. Sankappanavar All Rights Reserved This Edition may be copied for personal use This book is dedicated to our children Kurosh Phillip Burris Veena and Geeta and Sanjay Sankappanavar Preface to the Millennium Edition The original 1981 edition of A Course in Universal Algebra has now been LaTeXed so the authors could make the out-of-print Springer-Verlag Graduate Texts in Mathematics edition available once again, with corrections. The subject of Universal Algebra has flourished mightily since 1981, and we still believe that A Course in Universal Algebra offers an excellent introduction to the subject. Special thanks go to Lis D’Alessio for the superb job of LaTeXing this edition, and to NSERC for their support which has made this work possible. v Acknowledgments First we would like to express gratitude to our colleagues who have added so much vitality to the subject of Universal Algebra during the past twenty years. One of the original reasons for writing this book was to make readily available the beautiful work on sheaves and discriminator varieties which we had learned from, and later developed with H. Werner. Recent work of, and with, R. McKenzie on structure and decidability theory has added to our excitement, and conviction, concerning the directions emphasized in this book. In the late stages of polishing the manuscript we received valuable suggestions from M. Valeriote, W. Taylor, and the reviewer for Springer-Verlag. For help in proof-reading we also thank A. Adamson, M. Albert, D. Higgs, H. Kommel, G. Krishnan, and H. Riedel. A great deal of credit for the existence of the final product goes to Sandy Tamowski whose enthusiastic typing has been a constant inspiration. The Natural Sciences and