Polynomial Completeness in Algebraic Systems (Hardcover)

by Kalle Kaarli (Author), Alden F. Pixley (Author) "In Section 1.1 of this chapter we shall very briefly sketch some of the basic concepts about (universal) algebras, varieties of algebras, lattice theory, and..." (more)
Key Phrases: affine complete varieties, affine complete variety, affine completeness, Con A-compatible, Cross Lemma, Definition Let (more...)

Editorial Reviews

Review
This book gives a thorough, systematic treatment of various notions of polynomial completeness … the book is overdue as a reference for universal algebraists.
Mathematical Reviews, 2003a

This book gives a thorough, systematic treatment of various notions of polynomial completeness … the book is overdue as a reference for universal algebraists.
Mathematical Reviews, 2003a

Product 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.

Product Details

• Hardcover: 376 pages
• Publisher: Chapman & Hall/CRC; 1 edition (July 21, 2000)
• Language: English
• ISBN-10: 1584882034
• ISBN-13: 978-1584882039
• Product Dimensions: 9.5 x 6.5 x 1 inches
• Shipping Weight: 1.7 pounds (View shipping rates and policies)
• Average Customer Review: No customer reviews yet. Be the first.
• Amazon.com Sales Rank: #4,285,108 in Books (See Bestsellers in Books)