An Unusual Algebra

The present book is based on the lecture given by the author to senior pupils in Moscow on the 20th of April of 1966. The distinction between the material of the lecture and that of the book is that the latter includes exercises at the end of each section (the most difficult problems in the exercises are marked by an asterisk). At the end of the book are placed answers and hints to some of the problems. The reader is advised to solve most of the problems, if not all, because only after the problems have been solved can the reader be sure that he understands the subject matter of the book. The book contains some optional material (in particular, Sec. 7 and Appendix which are starred in the table of contents) that can be omitted in the first reading of the book. The corresponding parts of the text of the book are marked by one star at the beginning and by two stars at the end. However, in the second reading of the book it is advisable to study Sec. 7 since it contains some material important for practical applications of the theory of Boolean algebras. The bibliography given at the end of the book lists some books which can be of use to the readers who want to study the theory of Boolean algebras more thoroughly. The author is grateful to S. G. Gindikin for valuable advice and to F. I. Kizner for the thoroughness and initiative in editing the book.