Overview

M-Solid Varieties of Algebras provides a complete and systematic introduction to the fundamentals of the hyperequational theory of universal algebra, offering the newest results on M-solid varieties of semirings and semigroups. The book aims to develop the theory of M-solid varieties as a system of mathematical discourse that is applicable in several concrete situations. It applies the general theory to two classes of algebraic structures, semigroups and semirings. Both these varieties and their subvarieties play an important role in computer science. A unique feature of this book is the use of Galois connections to integrate different topics. Galois connections form the abstract framework not only for classical and modern Galois theory, involving groups, fields and rings, but also for many other algebraic, topological, ordertheoretical, categorical and logical theories. This concept is used throughout the whole book, along with the related topics of closure operators, complete lattices, Galois closed subrelations and conjugate pairs of completely additive closure operators.

Full Product Details

Author:   Jörg Koppitz ,  Klaus Denecke
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2006 ed.
Volume:   10
Dimensions:   Width: 15.50cm , Height: 2.00cm , Length: 23.50cm
Weight:   1.490kg
ISBN:  

9780387308043

ISBN 10:   0387308040
Pages:   342
Publication Date:   10 February 2006
Audience:   College/higher education ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Basic Concepts.- Closure Operators and Lattices.- M-Hyperidentities and M-solid Varieties.- Hyperidentities and Clone Identities.- Solid Varieties of Arbitrary Type.- Monoids of Hypersubstitutions.- M-Solid Varieties of Semigroups.- M-solid Varieties of Semirings.

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