Algebraic Theory of Semigroups, Volume II

This book, along with Volume I, 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 Sain's theory of the representations of an arbitrary semigroup by partial one-to-one transformations of a set, Redei's theory of finitely generated commutative semigroups, Howie's theory of amalgamated free products of semigroups, and 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.