Polynomial Completeness in Algebraic Systems / Edition 1

Polynomial Completeness in Algebraic Systems / Edition 1

by Kalle Kaarli, Alden F. Pixley
     
 

ISBN-10: 1584882034

ISBN-13: 9781584882039

Pub. Date: 07/21/2000

Publisher: Taylor & Francis

Boolean algebras have historically played a special role in the develo pment of the theory of general or "universal" algebraic systems, provi ding important links between algebra and analysis, set theory, mathema tical logic, and computer science. It is not surprising then that focu sing on specific properties of Boolean algebras has lead to new direct ions in

Overview

Boolean algebras have historically played a special role in the develo pment of the theory of general or "universal" algebraic systems, provi ding important links between algebra and analysis, set theory, mathema tical logic, and computer science. It is not surprising then that focu sing on specific properties of Boolean algebras has lead to new direct ions in universal algebra. In the first unified study of polynomial co mpleteness, Polynomial Completeness in Algebraic Systems focuses on an d systematically extends another specific property of Boolean algebras : the property of affine completeness. The authors present full proof that all affine complete varieties are congruence distributive and tha t they are finitely generated if and only if they can be presented usi ng only a finite number of basic operations. In addition to these impo rtant findings, the authors describe the different relationships betwe en the properties of lattices of equivalence relations and the systems of functions compatible with them.

Product Details

ISBN-13:
9781584882039
Publisher:
Taylor & Francis
Publication date:
07/21/2000
Pages:
376
Product dimensions:
6.40(w) x 9.50(h) x 1.00(d)

Table of Contents

ALGEBRAS, LATTICES, AND VARIETIES
Algebras, Languages, Clones, Varieties
Congruence Properties
CHARACTERIZATIONS OF EQUIVALENCE LATTICES
Introduction
Arithmeticity
Compatible Function Lifting
PRIMALITY AND GENERALIZATIONS
Primality and Functional Completeness
Near Unanimity Varieties
Arithmetical Varieties
Generalizations of Primality
Categorical Equivalence
AFFINE COMPLETE VARIETIES
Introduction and Instructive Examples
General properties
Varieties with a Finite Residual Bound
Locally Finite Affine Complete Varieties
POLYNOMIAL COMPLETENESS IN SPECIAL VARIETIES
Strictly Locally Affine Complete Algebras
Modules
Lattices
Algebras Based on Distributive Lattices
Semilattices
Miscellaneous Results

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