George Grätzer

The Congruences of a Finite Lattice (eBook, PDF)

A Proof-by-Picture Approach

• Format: PDF

Produktbeschreibung

The congruences of a lattice form the congruence lattice. In the past half-century, the study of congruence lattices has become a large and important field with a great number of interesting and deep results and many open problems. This self-contained exposition by one of the leading experts in lattice theory, George Grätzer, presents the major results on congruence lattices of finite lattices featuring the author's signature "Proof-by-Picture" method and its conversion to transparencies.

Key features:

* Includes the latest findings from a pioneering researcher in the field

* Insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensions

* Contains complete proofs, an extensive bibliography and index, and nearly 80 open problems

* Additional information provided by the author online at:

http://www.maths.umanitoba.ca/homepages/gratzer.html/

The book is appropriate for a one-semester graduate course in lattice theory, yet is also designed as a practical reference for researchers studying lattices.

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Produktdetails

• Verlag: Springer Basel AG
• Seitenzahl: 282
• Erscheinungstermin: 24. Mai 2007
• Englisch
• ISBN-13: 9780817644628
• Artikelnr.: 43728891

Autorenporträt

George A. Grätzer is a Hungarian-Canadian mathematician, specializing in lattice theory and universal algebra. He is also known for his books on LaTeX and his proof with E. Tamás Schmidt of the Grätzer-Schmidt theorem.

Inhaltsangabe

Part I: A Brief Introduction to Lattices.- Basic Concepts.- Special Concepts.- Congruences.- Planar Semimodular Lattices.- Part II: Some Special Techniques.- Chopped Lattices.- Boolean Triples.- Cube Extensions.- Part III: RTs.- Sectionally Complemented RT.- Minimal RT.- Semimodular RT.- Rectangular RT.- Modular RT.- Uniform RT.- Part IV: ETs.- Sectionally Complemented ET.- Semimodular ET.- Isoform ET.- Magic Wands.- Part V: Congruence Lattices of Two Related Lattices.- Sublattices.- Ideals.- Two Convex Sublattices.- Tensor Extensions.- Part VI: The Ordered Set of Principle Congruences.- The RT for Principal Congruences.- Minimal RTs.- Principal Congruence Representable Sets.- Isotone Maps.- Part VII: The Prime-Projectivity Lemma.- The Swing Lemma.- Fork Congruences.- Part VIII: The Six Congruence Properties of SPS Lattices.- Six Major Properties.