Lattices and Ordered Sets

AvSteven Roman

Häftad, Engelska, 2010

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Beskrivning

Lattice theory began in the early 1890s, when Richard Dedekind wanted to know the answer to the following question: Given three subgroups EF , and G of an abelian group K, what is the largest number of distinct subgroups that can be formed using these subgroups and the operations of intersection and sum (join), as in E?FßÐE?FÑ?GßE?ÐF?GÑ and so on?

Produktinformation

Utgivningsdatum:2010-10-29
Mått:155 x 235 x 21 mm
Vikt:490 g
Format:Häftad
Språk:Engelska
Antal sidor:305
Förlag:Springer-Verlag New York Inc.
ISBN:9781441927040

Utforska kategorier

Algebra inom Naturvetenskap och teknik

Recensioner i media

From the reviews: "This text ... deals with basic material in the areas of ordered sets and lattices and is aimed at advanced undergraduate or (more likely) beginning graduate students. ... The choice and coverage of the material involved is excellent and the presentation is pleasantly lucid ... . Throughout the text the arguments are clear and sound, and at the end of each chapter there is a good selection of exercises to whet the reader's appetite. ... this is a worthy addition to the lattice theory literature." (T. S. Blyth, Mathematical Reviews, Issue 2009 f)

Innehållsförteckning

Basic Theory.- Partially Ordered Sets.- Well-Ordered Sets.- Lattices.- Modular and Distributive Lattices.- Boolean Algebras.- The Representation of Distributive Lattices.- Algebraic Lattices.- Prime and Maximal Ideals; Separation Theorems.- Congruence Relations on Lattices.- Topics.- Duality for Distributive Lattices: The Priestley Topology.- Free Lattices.- Fixed-Point Theorems.