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Galois Connections and Applications / Edition 1

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This book presents the main ideas of General Galois Theory as a generalization of Classical Galois Theory. It sketches the development of Galois connections through the last three centuries. Examples of Galois connections as powerful tools in Category Theory and Universal Algebra are given. Applications of Galois connections in Linguistic and Data Analysis are presented.

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Editorial Reviews

From the Publisher
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"The book under review is the first one fully dedicated to Galois connections and adjunctions. … I recommend this valuable collection to everybody involved in algebraic research and/or teaching algebra in higher education." (Béla Csákány, Acta Scientiarum Mathematicarum, Vol. 71, 2005)

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Product Details

  • ISBN-13: 9781402018978
  • Publisher: Springer Netherlands
  • Publication date: 3/31/2004
  • Series: Mathematics and Its Applications (closed) Series , #565
  • Edition description: 2004
  • Edition number: 1
  • Pages: 502
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.13 (d)

Table of Contents

M. Erné; Adjunctions and Galois Connections: Origins, History and Development
G. Janelidze; Categorical Galois Theory: Revision and Some Recent Developments
M. Erné; The Polarity between Approximation and Distribution
K. Denecke, S.L. Wismath; Galois Connections and Complete Sublattices
R. Pöschel; Galois Connections for Operations and Relations
K. Kaarli; Galois Connections and Polynomial Completeness
K. Glazek, St. Niwczyk; Q-Independence and Weak Automorphisms
A. Szendrei; A Survey of Clones Closed Under Conjugation
P. Burmeister; Galois Connections for Partial Algebras
K. Denecke, S.L. Wismath; Complexity of Terms and the Galois Connection Id-Mod
J. Lambek; Iterated Galois Connections in Arithmetic and Linguistics
I. Chajda, R. Halas; Deductive Systems and Galois Connections
J. Slapal; A Galois Correspondence for Digital Topology
W. Gähler; Galois Connections in Category Theory, Topology and Logic
R. Wille; Dyadic Mathematics - Abstractions from Logical Thought

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