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 material.
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