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The q-theory of Finite Semigroups
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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. The book 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; and presents over 70 research problems, most new, and hundreds of exercises. For newcomers, there is an appendix on elementary finite semigroup theory. It also features extensive bibliography and index.
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Subject categories
- Academic > Mathematics > Algebra > Semigroups
- Academic > Mathematics > General > Vinogradov, Ivan Matveevich, 1891-
- Academic > Mathematics > General > Mathematics; Periodicals
- Academic > Mathematics > General > Mathematics; Study and teaching; Audio-visual aids
- Mathematics > Algebra
- Mathematics > Logic
ISBNs
0387097813
9780387097800
9780387097817