Topic
Bicyclic semigroup
About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.
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Book•
01 Jan 1995
TL;DR: Inverse semigroups as discussed by the authors are a subclass of regular semigroup classes and can be seen as semigroup amalgamations of semigroup groups, which is a special case of regular semiigroups.
Abstract: 1. Introductory ideas 2. Green's equivalences regular semigroups 3. 0-simple semigroups 4. Completely regular semigroups 5. Inverse semigroups 6. Other classes of regular semigroups 7. Free semigroups 8. Semigroup amalgams References List of symbols
1,979 citations
Book•
01 Mar 1984
TL;DR: Gilmer's "Commutative Semigroup Rings" as mentioned in this paper was the first exposition of the basic properties of semigroup rings, focusing on the interplay between semigroups and rings, thereby illuminating both of these important concepts in modern algebra.
Abstract: "Commutative Semigroup Rings" was the first exposition of the basic properties of semigroup rings. Gilmer concentrates on the interplay between semigroups and rings, thereby illuminating both of these important concepts in modern algebra.
452 citations
TL;DR: In this paper, a new monoid structure for Artin groups associated with finite Coxeter systems is proposed, which is a Garside monoid, and several equivalent constructions are given.
Abstract: We study a new monoid structure for Artin groups associated with finite Coxeter systems. Like the classical positive braid monoid, the new monoid is a Garside monoid. We give several equivalent constructions: algebraically, the new monoid arises when studying Coxeter systems in a “dual” way, replacing the pair ( W , S ) by ( W , T ), with T the set of all reflections; geometrically, it arises when looking at the reflection arrangement from a certain basepoint. In the type A case, we recover the monoid constructed by Birman, Ko and Lee.
330 citations
Book•
01 Jan 1991
TL;DR: In this article, free inverse semigroups and the theorems of McAlister Biordered sets Zigzags and their applications are discussed. But they do not cover the application of ZigZags in word problems.
Abstract: Fundamentals Free inverse semigroups and the theorems of McAlister Biordered sets Zigzags and their applications Semigroup diagrams and word problems Combinatorial aspects of transformation semigroups References Glossary of notation Index.
329 citations
Book•
12 May 2009
TL;DR: The q-theory of finite semigroups as mentioned in this paper is a theory that provides a unifying approach to finite semigroup theory via quantization, and it is the only contemporary exposition of the complete theory of the complexity of finite semiigroups.
Abstract: 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.
325 citations