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Cover: 9780387789002 | Lattices and Ordered Sets | Steven Roman | Buch | xv | Englisch | 2008
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Lattices and Ordered Sets
Buch von Steven Roman
Sprache: Englisch

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Beschreibung
This book is intended to be a thorough introduction to the subject of order and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. This is a book on pure mathematics: I do not discuss the applications of lattice theory to physics, computer science or other disciplines. 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? In lattice-theoretic terms, this is the number of elements in the relatively free modular lattice on three generators. Dedekind [15] answered this question (the answer is #)) and wrote two papers on the subject of lattice theory, but then the subject lay relatively dormant until Garrett Birkhoff, Oystein Ore and others picked it up in the 1930s. Since then, many noted mathematicians have contributed to the subject, including Garrett Birkhoff, Richard Dedekind, Israel Gelfand, George Grätzer, Aleksandr Kurosh, Anatoly Malcev, Oystein Ore, Gian-Carlo Rota, Alfred Tarski and Johnny von Neumann.
This book is intended to be a thorough introduction to the subject of order and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. This is a book on pure mathematics: I do not discuss the applications of lattice theory to physics, computer science or other disciplines. 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? In lattice-theoretic terms, this is the number of elements in the relatively free modular lattice on three generators. Dedekind [15] answered this question (the answer is #)) and wrote two papers on the subject of lattice theory, but then the subject lay relatively dormant until Garrett Birkhoff, Oystein Ore and others picked it up in the 1930s. Since then, many noted mathematicians have contributed to the subject, including Garrett Birkhoff, Richard Dedekind, Israel Gelfand, George Grätzer, Aleksandr Kurosh, Anatoly Malcev, Oystein Ore, Gian-Carlo Rota, Alfred Tarski and Johnny von Neumann.
Zusammenfassung

Written in an appealing style

Will become a standard text and an invaluable guide

Contains a plethora of exercises, examples, and illustrations

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2008
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xv
305 S.
43 s/w Illustr.
43 s/w Zeichng.
ISBN-13: 9780387789002
ISBN-10: 0387789006
Sprache: Englisch
Herstellernummer: 12208609
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Roman, Steven
Hersteller: Springer US
Springer New York
Springer US, New York, N.Y.
Maße: 241 x 160 x 23 mm
Von/Mit: Steven Roman
Erscheinungsdatum: 19.09.2008
Gewicht: 0,653 kg
Artikel-ID: 101734595
Zusammenfassung

Written in an appealing style

Will become a standard text and an invaluable guide

Contains a plethora of exercises, examples, and illustrations

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2008
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xv
305 S.
43 s/w Illustr.
43 s/w Zeichng.
ISBN-13: 9780387789002
ISBN-10: 0387789006
Sprache: Englisch
Herstellernummer: 12208609
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Roman, Steven
Hersteller: Springer US
Springer New York
Springer US, New York, N.Y.
Maße: 241 x 160 x 23 mm
Von/Mit: Steven Roman
Erscheinungsdatum: 19.09.2008
Gewicht: 0,653 kg
Artikel-ID: 101734595
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