Galois Connections and Applications

ISBN-13: 9789048165407 / Angielski / Miękka / 2010 / 502 str.

K. Denecke; M. Erne; S. L. Wismath

Opis

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.

Recenzje

From the reviews:

"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)

Spis treści

Preface 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 Index