Finite Semigroups and Universal Algebra

Download or read book Finite Semigroups and Universal Algebra written by Jorge Almeida and published by World Scientific. This book was released on 1995-01-27 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by applications in theoretical computer science, the theory of finite semigroups has emerged in recent years as an autonomous area of mathematics. It fruitfully combines methods, ideas and constructions from algebra, combinatorics, logic and topology. In simple terms, the theory aims at a classification of finite semigroups in certain classes called “pseudovarieties”. The classifying characteristics have both structural and syntactical aspects, the general connection between them being part of universal algebra. Besides providing a foundational study of the theory in the setting of arbitrary abstract finite algebras, this book stresses the syntactical approach to finite semigroups. This involves studying (relatively) free and profinite free semigroups and their presentations. The techniques used are illustrated in a systematic study of various operators on pseudovarieties of semigroups. Contents:Finite Universal Algebra:Elements of Universal AlgebraOrder and TopologyFinite AlgebrasDecidabilityFinite Semigroups and Monoids:PreliminariesPermutativityOperators Relating Semigroups and MonoidsSemigroups Whose Regular D-Classes are SubsemigroupsThe JoinThe Semidirect ProductThe PowerFactorization of Implicit OperationsOpen Problems Readership: Mathematicians and computer scientists. keywords:Inite Semigroups;Finite Monoids;Universal Algebra;Recognizable Languages;Pseudovarieties;Pseudoidentities;Implicit Operations;Relatively Free Profinite Semigroups;Semidirect Products;Power Semigroups “This book is devoted to an exciting new field where author has made important contributions, and thus it is a most welcome addition to the existing literature. It will find its place on the bookshelves of many a specialist in semigroups, as well as species of algebraists and computer scientists, including graduate students.” Semigroup Forum “The book … constitutes an important contribution to the most active part of the present theory of finite semigroups. All overwhelming majority of the results included in it is very new and has been scattered over journals so far. The book does not cover all of the theory of semigroup … but it is extremely rich in material and ideas presented with skill and dedication. The book has already influenced the area essentially, and its influence will certainly grow … I think the book is a must for researchers in the area but it is also very useful for all those who want to trace modern developments in the theory of semigroups.” Mathematics Abstracts