Inverse element

Abstract: This book, along with volume I, which appeared previously, presents a survey of the structure and representation theory of semi groups. Volume II goes more deeply than was possible in volume I into 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 semi group 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 semi group by partial one-to-one transformations of a set, L. Redei's theory of finitely generated commutative semi groups, J. M. Howie's theory of amalgamated free products of semi groups, and E. J. Tully's theory of representations of a semi group by transformations of a set. Also a full account is given of Malcev's theory of the congruences on a full transformation semi group.

Abstract: Introduction to inverse semigroups elementary properties of inverse semigroups Ehresmann's maximum enlargement theorem presentations of inverse monoids inverse semigroups and formal languages the type II theorem complements.

Abstract: 1. Introduction.- 2. Inverse Semigroups and Locally Compact Groupoids.- 2.1 Inverse semigroups.- 2.2 Locally compact and r-discrete groupoids.- 2.3 Lie groupoids.- 3. Groupoid C*-Algebras and Their Relation to Inverse Semigroup Covariance C*-Algebras.- 3.1 Representation theory for locally compact groupoids.- 3.2 Representation theory for groupoids that are r-discrete, and their inverse semigroups of open G-sets.- 3.3 Groupoid and covariance C*-algebras.- 4. The Groupoid C*-Algebras of Inverse Semigroups.- 4.1 Introduction.- 4.2 Examples of inverse semigroups and their associated groupoids.- 4.3 The universal groupoid of an inverse semigroup.- 4.4 Inverse semigroup universal and reduced C*-algebras as groupoid C*-algebras.- 4.5 Amenability of the von Neumann algebra of an inverse semigroup.- Appendix A. Amenability for Inverse Semigroups.- Appendix B. Groupoid Amenability and Locally Compact Groups.- Appendix C. The Measurability of Fg.- Appendix D. Ind ? as an Induced Representation.- Appendix E. Guichardet's Disintegration Theorem.- Appendix F. Some Differential Topology.- Index of Terms.- Index of Symbols.