q-theory of Finite Semigroups (eBook)

John Rhodes, Benjamin Steinberg (Autoren)

eBook Download: PDF

2009
XXI, 666 Seiten
Springer US (Verlag)
978-0-387-09781-7 (ISBN)

Infos

This comprehensive, encyclopedic text in four parts aims to give the reader - from the graduate student to the researcher/practitioner - a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research. The q-theory of Finite Semigroups presents important techniques and results, many for the first time in book form, thereby updating and modernizing the semigroup theory literature.

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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.

Inhalt

Preface 6
Contents 12
List of Tables 18
List of Figures 19
Introduction 20
Part I The q -operator and Pseudovarieties of Relational Morphisms 32
Part II Complexity in Finite Semigroup Theory 230
Part III The Algebraic Lattice of Semigroup Pseudovarieties 441
Part IV Quantales, Idempotent Semirings, Matrix Algebras and the Triangular Product 535

Produkt-Details

• Erscheint lt. Verlag: 5.4.2009
• Reihe/Serie: Springer Monographs in Mathematics
• Reihe/Serie: Springer Monographs in Mathematics
• Zusatzinfo: XXII, 666 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Technik
• Schlagworte: Algebra • Boolean algebra • Complexity • group theory • lattice • Matrix • matrix theory
• ISBN-10: 0-387-09781-3 / 0387097813
• ISBN-13: 978-0-387-09781-7 / 9780387097817