The q-theory of Finite Semigroups

by John Rhodes, Benjamin Steinberg

Discoveries in finite semigroups have influenced several mathematical fields, including theoretical computer science, tropical algebra via matrix theory with coefficients in semirings, and other areas of modern algebra. This comprehensive, encyclopedic text will provide the reader - from the graduate student to the researcher/practitioner - with a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research.

Key features: (1) Develops q-theory, a new theory that provides a unifying approach to finite semigroup theory via quantization; (2) Contains the only contemporary exposition of the complete theory of the complexity of finite semigroups; (3) Introduces spectral theory into finite semigroup theory; (4) Develops the theory of profinite semigroups from first principles, making connections with spectra of Boolean algebras of regular languages; (5) Presents over 70 research problems, most new, and hundreds of exercises.

Additional features: (1) For newcomers, an appendix on elementary finite semigroup theory; (2) Extensive bibliography and index.

The q-theory of Finite Semigroups presents important techniques and results, many for the first time in book form, and thereby updates and modernizes the literature of semigroup theory.

Genres: Mathematics

666 pages, Unknown Binding

First published December 17, 2008

About the author

John Rhodes is the award winning author of the Breaking Point series set in the Battle of Britain, and of the Thomas Ford ‘cozy’ detective series. Rhodes graduated from Cambridge University where he studied history. His focus on World War II stems from his earliest memories—he was born while his father was serving at an RAF Fighter Command airfield, and he grew up in London, where, he says, the shells of bombed-out buildings ‘served as our adventure playgrounds.’

He is currently working on a third book in the Breaking Point series, set in Malta in 1942, and another ‘whodunit’ murder case for Thomas Ford to solve.