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Algebras and Orders

  • Book
  • © 1993

Overview

Editors:
  1. Ivo G. Rosenberg

    1. Département de mathématiques et de statistique, Université de Montréal, Montréal, Canada

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  2. Gert Sabidussi

    1. Département de mathématiques et de statistique, Université de Montréal, Montréal, Canada

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Nato Science Series C: (ASIC, volume 389)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Partial Algebras — An Introductory Survey

    • Peter Burmeister
    Pages 1-70

  3. Duality Theory on Ten Dollars a Day

    • Brian A. Davey
    Pages 71-111

  4. Algebraic Ordered Sets and Their Generalizations

    • Marcel Erné
    Pages 113-192

  5. A Boolean Formalization of Predicate Calculus

    • Isidore Fleischer
    Pages 193-198

  6. Lectures on Free Lattices

    • Ralph Freese
    Pages 199-237

  7. A Survey of Boolean Algebras with Operators

    • Bjarni Jónsson
    Pages 239-286

  8. Essentially Minimal Groupoids

    • Hajime Machida, Ivo G. Rosenberg
    Pages 287-316

  9. Functional and Affine Completeness and Arithmetical Varieties

    • Alden F. Pixley
    Pages 317-357

  10. Reading, Drawing, and Order

    • Ivan Rival
    Pages 359-404

  11. Hyperidentities

    • Dietmar Schweigert
    Pages 405-506

  12. Abstract Clone Theory

    • Walter Taylor
    Pages 507-530

  13. Back Matter

    Pages 531-553
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Keywords

About this book

In the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "Algebras and Orders" as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation. This book contains the contributions of the invited speakers. Universal algebra- which established itself only in the 1930's- grew from traditional algebra (e.g., groups, modules, rings and lattices) and logic (e.g., propositional calculus, model theory and the theory of relations). It started by extending results from these fields but by now it is a well-established and dynamic discipline in its own right. One of the objectives of the ASI was to cover a broad spectrum of topics in this field, and to put in evidence the natural links to, and interactions with, boolean algebra, lattice theory, topology, graphs, relations, automata, theoretical computer science and (partial) orders. The theory of orders is a relatively young and vigorous discipline sharing certain topics as well as many researchers and meetings with universal algebra and lattice theory. W. Taylor surveyed the abstract clone theory which formalizes the process of compos­ ing operations (i.e., the formation of term operations) of an algebra as a special category with countably many objects, and leading naturally to the interpretation and equivalence of varieties.

Editors and Affiliations

  • Département de mathématiques et de statistique, Université de Montréal, Montréal, Canada

    Ivo G. Rosenberg, Gert Sabidussi

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