The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, BrasilWalter D. Neumann, Columbia University, New York, USAMarkus J. Pflaum, University of Colorado, Boulder, USADierk Schleicher, Jacobs University, Bremen, GermanyKatrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019)Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019)Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019)Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021)Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
Rezensionen / Stimmen
"The authors of this book are well-known specialists in the area of homological classification of monoids. The presentation is extremely clear and incisive. Without a doubt, the book could serve as a textbook for a very good graduate course on representation theory of monoids, homological algebra and category theory." Mathematical Reviews "The material of the book is well organised and suitable for a broad audience interested in monoids, acts, non-abelian categories as well as in formal languages, automata theory and other applications of semigroups. The book is comprehensive and self-contained and can be used both as study material for courses on representation theory on monoids, homological algebra and category theory, and as a handbook for students and researchers in the area. This is why the book should not be missing in any library of the faculty of mathematics of any university." Zentralblatt für Mathematik
Reihe
Auflage
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
US School Grade: College Graduate Student
Maße
Höhe: 246 mm
Breite: 175 mm
Dicke: 34 mm
Gewicht
ISBN-13
978-3-11-015248-7 (9783110152487)
Schweitzer Klassifikation
Elementary properties of monoids, acts and categories: sets and relations; groupoids, semigroups and monoids; some classes of semigroups; acts over monoids (monoid automata); decompositions and components; categories; functors. Constructions: products and coproducts; pullbacks and pushouts; free objects and generators; cofree objects and generators; tensor products; wreath products of monoids and acts; the wreath product of a monoid with a small category. Classes of acts: injective acts; divisible acts; principally weakly injective acts; fg-weakly injective acts; absolutely pure acts; cogenerators and overview; torsion free acts; flatness of acts and related properties; principally weakly flat acts; weakly flat acts; flat acts; acts satisfying condition (P); acts satisfying condition (E); equalizer flat acts; pullback flat acts and overview; projective acts; generators; regular acts and overview. Homological classification of monoids: principal weak injectivity; on fg-weak injectivity; weak injectivity; absolute purity; injectivity and overview; torsion freeness and principal weak flatness; flatness; condition (P); strong flatness; projectivity; projective generators; freeness and overview; regularity of acts. Equivalence and duality: adjoint functors; categories equivalent to act - S Morita equivalence of monoids; endomorphism monoids of generators; on morita duality.
