Algebra in the Stone-Cech Compactification : Theory and Applications

This is the second revised and extended edition of the successful book on the algebraic structure of the Stone-Cech compactification of a discrete semigroup and its combinatorial applications, primarily in the field known as Ramsey Theory. There has been very active research in the subject dealt with by the book in the 12 years which is now included in this edition.

This book is a self-contained exposition of the theory of compact right semigroups for discrete semigroups and the algebraic properties of these objects. The methods applied in the book constitute a mosaic of infinite combinatorics, algebra, and topology. The reader will find numerous combinatorial applications of the theory, including the central sets theorem, partition regularity of matrices, multidimensional Ramsey theory, and many more.

"The present book is the first devoted to an extensive study of the algebraic structure of βS and the many applications thereof; it is an exciting book, written - and very well written - by two mathematicians who are eminently qualified two write it, and it is essentially self-contained, requiring only that the reader come to it with the basic concepts of first graduate courses in algebra, analysis and topology. […] I recommend this book highly; it will be very useful, both to researchers and to students. Its index, list of symbols and up-to-date bibliography are very helpful […]."
Paul Milnes, Zentralblatt MATH / 1998

"The authors present a self-contained exposition […]. The book under review is written by two mathematicians who have contributed in a decisive way to this rapidly expanding area […] and provides a unique opportunity to obtain a ''colorful'' panoramic view of the subject."
Michael Tkacenko, MathSciNet / 1999