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Catalogue Information
Field name	Details
Dewey Class	512.27
Title	The q-theory of Finite Semigroups ([Ebook]) / by John Rhodes, Benjamin Steinberg.
Author	Rhodes, John
Added Personal Name	Steinberg, Benjamin
Other name(s)	SpringerLink (Online service)
Publication	Boston, MA : Springer US , 2009.
Physical Details	XXII, 666 pages : online resource.
Series	Springer monographs in mathematics 1439-7382
ISBN	9780387097817
Summary Note	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 â from the graduate student to the researcher/practitioner â with a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research. Key features: * Develops q-theory, a new theory that provides a unifying approach to finite semigroup theory via quantization; * Contains the only contemporary exposition of the complete theory of the complexity of finite semigroups; * Introduces spectral theory into finite semigroup theory; * Develops the theory of profinite semigroups from first principles, making connections with spectra of Boolean algebras of regular languages; * Presents over 70 research problems, most new, and hundreds of exercises. Additional features: * For newcomers, an appendix on elementary finite semigroup theory; * 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.:
Contents note	Preface -- Introduction -- 1. Foundations for Finite Semigroup Theory -- 2. The q-operator -- 3.The Equational Theory -- 4. The Complexity of Finite Semigroups -- 5. Two-Sided Complexity and the Complexity of Operators -- 6. Algebraic Lattices, Continuous Lattices and Closure Operators -- 7. The Abstract Spectral Theory of PV -- 8. Quantales -- 9. The Triangular Product and Decomposition Results for Semirings -- A. The Green-Rees Local Structure Theory -- B. Tables on Preservation of Sups and Infs -- List of Problems -- References -- Table of Pseudovarieties -- Table of Operators and Products -- Index of Notation -- Author Index -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/b104443
Links to Related Works	Subject References: Algebra . Computer Science . General Algebraic Systems . Group theory . Group Theory and Generalizations . Mathematical Logic and Formal Languages . Mathematics . Order, Lattices, Ordered Algebraic Structures . Semigroups . Authors: author . Rhodes, John . Steinberg, Benjamin . Corporate Authors: SpringerLink (Online service) . Series: Springer monographs in mathematics . Classification: 512.27 . 512.27 (DDC 23) .

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The q-theory of Finite Semigroups

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