Algebra in the Stone-Cech Compactification

"Algebra in the Stone-Cech Compactification" is a comprehensive and revised edition that addresses the algebraic structure of the Stone-Cech compactification of discrete semigroups. This second, expanded edition integrates twelve years of active research and provides a detailed analysis of the theoretical foundations and practical applications in Ramsey theory. The book is designed to serve as a standalone introduction to the theory of compact right semigroups for discrete semigroups, illuminating the algebraic properties of these structures. The applied methods combine elements of infinite combinatorics, algebra, and topology, offering readers valuable insights into numerous combinatorial applications of the theory. These include, among others, the central set theorem, the partition regularity of matrices, and multidimensional Ramsey theory.