This book introduces recently developed ideas and techniques in semigroup theory to provide a handy reference guide previously unavailable in a single volume. The opening chapter provides sufficient background to enable the reader to follow any of the subsequent chapters, and would by itself be suitable for a first course in semigroup theory. The second chapter gives an account of free inverse semigroups leading to proofs of the McAlister P-theorems. Subsequent
chapters have the underlying theme of diagrams and mappings, and the new material includes the theory of biordered sets of Nambooripad and Easdown, the semigroup diagrams of Remmers and Jackson with
applications to the one-relator, and other word problems, a short proof of Isbell's Zigzag theorem with applications to epimorphisms and amalgams, together with combinatorial, probabalistic and graphical techniques used to prove results including Schein's Covering Theorem and Howie's Gravity Formula for finite full transformation semigroups. Nearly two hundred exercises serve the dual purpose of illustrating the richness of the subject while allowing the reader to come to grips with the
'This book introduces recently developed ideas in semigroup theory and serves to provide a handy reference guide previously unavailable in a single volume.'
L'Enseignement Mathématique, 1992
'fresh and well-written book ... Graphical and diagram arguments make proofs intuitive and elegant.'
J. Henno, Zentralblatt für Mathematik und ihre Grenzgebiete Mathematics Abstracts
'Nearly two thirds of the content appear here for the first time in book-form, written in a fresh and stimulating style. New emphases and new connections in the presentation make this book a pleasure to read.'
H. Mitsch, Monatshelfe für Mathematik, Vol. 116, No. 2, 1993
'Refreshingly lively and down-to-earth, with many new results (using semigroup diagrams to treat word problems) and new proofs, e.g., of Isbell's zigzag theorem, which is then applied to study amalgams.'
Mathematika, 39 (1992)
`The book is written with clarity, the proofs and arguments are usually presented in a brief and elegant way, and even familiar things are often viewed from a fresh perspective. Although the pace is fast, this enviably crisp and clear exposition is a pleasure to read. It will be very useful for semigroup theorists and graduate students as well as for specialists in other fields who may use it as a reference. Altogether, this is a most welcome addition to
the available monographs on semigroups.'
Boris M. Schein, Semigroup Forum Vol. 49 (1994)
Fundamentals; Free inverse semigroups and the theorems of McAlister; Biordered sets; Zigzags and their applications; Semigroup diagrams and word problems; Combinatorial aspects of transformation semigroups; References; Glossary of notation; Index.