Polynomial Completeness in Algebraic Systems
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A01=Alden F. Pixley
A01=Kalle Kaarli
Abelian Group
advanced algebraic systems research
affine completeness
Arithmetical Variety
Author_Alden F. Pixley
Author_Kalle Kaarli
Boolean Algebras
Bounded Distributive Lattice
Category=PBF
Cd Variety
Compatible Function
congruence distributive varieties
Congruence Lattice
Congruence Primal
Distributive Lattice
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
equivalence lattices
Finite Algebra
Finite Height
Finitely Generated
finitely generated algebras
Functionally Complete
Inverse Semigroup
Kleene Algebras
Local Polynomial
Locally Finite
mathematical logic applications
Order Language
Primal Algebras
Principal Congruences
Principal Ideal
Proper Subalgebras
Residually Finite
Structure Semilattice
Subdirect Product
universal algebra
Product details
- ISBN 9780367398330
- Weight: 453g
- Dimensions: 156 x 234mm
- Publication Date: 05 Sep 2019
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Paperback
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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.
Kaarli, Kalle; Pixley, Alden F.
