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Author:   Mati Kilp ,  Ulrich Knauer ,  Alexander V. Mikhalev
Publisher:   De Gruyter
Imprint:   De Gruyter
Edition:   Reprint 2011
Volume:   29
Dimensions:   Width: 17.00cm , Height: 3.50cm , Length: 24.00cm
Weight:   1.028kg
ISBN:  

9783110152487

ISBN 10:   3110152487
Pages:   546
Publication Date:   22 March 2000
Recommended Age:   College Graduate Student
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

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.

Reviews

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 fur Mathematik

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 f r Mathematik

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 fur Mathematik

"""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 f�r Mathematik"

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