The Equational Classes Generated by Single Functionally Precomplete Algebras

The Equational Classes Generated by Single Functionally Precomplete Algebras
Author: Arthur Knoebel
Publisher: American Mathematical Soc.
Total Pages: 93
Release: 1985
Genre: Mathematics
ISBN: 0821823337
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Ivo Rosenberg determined all finite, finitary, functionally precomplete algebras; he split them up naturally into six classes according to the kind of relation which is preserved by the polynomials of each such algebra. The purpose of this memoir is to locate these algebras in the equational lattice.

Sheaves of Algebras over Boolean Spaces

Sheaves of Algebras over Boolean Spaces
Author: Arthur Knoebel
Publisher: Springer Science & Business Media
Total Pages: 336
Release: 2011-12-15
Genre: Mathematics
ISBN: 0817642188
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This unique monograph building bridges among a number of different areas of mathematics such as algebra, topology, and category theory. The author uses various tools to develop new applications of classical concepts. Detailed proofs are given for all major theorems, about half of which are completely new. Sheaves of Algebras over Boolean Spaces will take readers on a journey through sheaf theory, an important part of universal algebra. This excellent reference text is suitable for graduate students, researchers, and those who wish to learn about sheaves of algebras.

Function Algebras on Finite Sets

Function Algebras on Finite Sets
Author: Dietlinde Lau
Publisher: Springer Science & Business Media
Total Pages: 668
Release: 2006-11-23
Genre: Mathematics
ISBN: 3540360239
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Function Algebras on Finite Sets gives a broad introduction to the subject, leading up to the cutting edge of research. The general concepts of the Universal Algebra are given in the first part of the book, to familiarize the reader from the very beginning on with the algebraic side of function algebras. The second part covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, and clone theory.

Hyperidentities and Clones

Hyperidentities and Clones
Author: Klaus Denecke
Publisher: CRC Press
Total Pages: 334
Release: 2000-08-08
Genre: Mathematics
ISBN: 9789056992354
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Theories and results on hyperidentities have been published in various areas of the literature over the last 18 years. Hyperidentities and Clones integrates these into a coherent framework for the first time. The author also includes some applications of hyperidentities to the functional completeness problem in multiple-valued logic and extends the general theory to partial algebras. The last chapter contains exercises and open problems with suggestions for future work in this area of research. Graduate students and mathematical researchers will find Hyperidentities and Clones a thought-provoking and illuminating text that offers a unique opportunity to study the topic in one source.

Universal Algebra and Coalgebra

Universal Algebra and Coalgebra
Author: Klaus Denecke
Publisher: World Scientific
Total Pages: 291
Release: 2009
Genre: Mathematics
ISBN: 9812837450
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The purpose of this book is to study the structures needed to model objects in universal algebra, universal coalgebra and theoretical computer science. Universal algebra is used to describe different kinds of algebraic structures, while coalgebras are used to model state-based machines in computer science.The connection between algebras and coalgebras provides a way to connect static data-oriented systems with dynamical behavior-oriented systems. Algebras are used to describe data types and coalgebras describe abstract systems or machines.The book presents a clear overview of the area, from which further study may proceed.