by Jorge Almeida (Univ. Porto)

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.

• Finite Universal Algebra:
  • Elements of Universal Algebra
  • Order and Topology
  • Finite Algebras
  • Decidability
• Finite Semigroups and Monoids:
  • Preliminaries
  • Permutativity
  • Operators Relating Semigroups and Monoids
  • Semigroups Whose Regular D-Classes are Subsemigroups
  • The Join
  • The Semidirect Product
  • The Power
  • Factorization of Implicit Operations
• Open Problems