The algebraic theory of semigroups. Vol.2

The material in this volume was presented in a second-year graduate course at Tulane University, during the academic year 1958–1959. The book aims at being largely self-contained, but it is assumed that the reader has some familiarity with sets, mappings, groups, and lattices. Only in Chapter 5 will more preliminary knowledge be required, and even there the classical definitions and theorems on the matrix representations of algebras and groups are summarized. This book, along with Volume I, which appeared previously, presents a survey of the structure and representation theory of semigroups. Volume II goes more deeply than was possible in Volume I into the theories of minimal ideals in a semigroup, inverse semigroups, simple semigroups, congruences on a semigroup, and the embedding of a semigroup in a group. Among the more important recent developments of which an extended treatment is presented are B. M. Sain's theory of the representations of an arbitrary semigroup by partial one-to-one transformations of a set, L. Redei's theory of finitely generated commutative semigroups, J. M. Howie's theory of amalgamated free products of semigroups, and E. J. Tully's theory of representations of a semigroup by transformations of a set. Also a full account is given of Malcev's theory of the congruences on a full transformation semigroup. Presents a survey of the structure and representation theory of semi groups. This book describes the theories of minimal ideals in a semi group, inverse semi groups, simple semi groups, congruences on a semi group, and the embedding of a semigroup in a group. Presents material on sets, mappings, groups, and lattices. This book summarizes classical definitions and theorems on the matrix representations of algebras and groups.