Description
Polynomial Completeness in Algebraic Systems
Authors: Kaarli Kalle, Pixley Alden F.
Language: EnglishSubjects for Polynomial Completeness in Algebraic Systems:
Keywords
Proper Subalgebras; Finite Algebra; Compatible Function; Principal Congruences; Arithmetical Variety; Congruence Lattice; Primal Algebras; Subdirect Product; Finitely Generated; Congruence Primal; Cd Variety; Inverse Semigroup; Boolean Algebras; Kleene Algebras; Bounded Distributive Lattice; Abelian Group; Structure Semilattice; Local Polynomial; Locally Finite; Principal Ideal; Residually Finite; Functionally Complete; Distributive Lattice; Finite Height; Order Language
Publication date: 09-2019
· 15.6x23.4 cm · Paperback
Approximative price 208.65 €
Subject to availability at the publisher.
Add to cart the book of Kaarli Kalle, Pixley Alden F.Publication date: 07-2000
376 p. · 15.6x23.4 cm · Paperback
Description
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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.