Polynomial Completeness in Algebraic Systems: 1st Edition (Paperback) book cover

Polynomial Completeness in Algebraic Systems

1st Edition

By Kalle Kaarli, Alden F. Pixley

Chapman and Hall/CRC

376 pages

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pub: 2019-09-05
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Description

Boolean algebras have historically played a special role in the development of the theory of general or "universal" algebraic systems, providing important links between algebra and analysis, set theory, mathematical logic, and computer science. It is not surprising then that focusing on specific properties of Boolean algebras has lead to new directions in universal algebra.

In the first unified study of polynomial completeness, Polynomial Completeness in Algebraic Systems focuses on and 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 that they are finitely generated if and only if they can be presented using only a finite number of basic operations. In addition to these important findings, the authors describe the different relationships between the properties of lattices of equivalence relations and the systems of functions compatible with them.

An introductory chapter surveys the appropriate background material, exercises in each chapter allow readers to test their understanding, and open problems offer new research possibilities. Thus Polynomial Completeness in Algebraic Systems constitutes an accessible, coherent presentation of this rich topic valuable to both researchers and graduate students in general algebraic systems.

Table of Contents

Algebras, Lattices, and Varieties. Characterizations of Equivalence Lattices. Primality and Generalizations. Affine Complete Varieties. Polynomial Completeness in Special Varieties.

About the Authors

Kaarli, Kalle; Pixley, Alden F.

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT002000
MATHEMATICS / Algebra / General
MAT028000
MATHEMATICS / Set Theory