Steven Roman

Lattices and Ordered Sets (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book is intended to be a thorough introduction to the subject of ordered sets 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.

The book has an excellent choice of topics, including a chapter on well ordering and ordinal numbers, which is not usually found in other texts. The approach is user-friendly and the presentation is lucid. There are more than 240 carefully chosen exercises.

Topic coverage includes: modular, semimodular and distributive lattices, boolean algebras, representation of distributive lattices, algebraic lattices, congruence relations on lattices, free lattices, fixed-point theorems, duality theory and more.

Steven Roman is the author of many successful textbooks, including Advanced Linear Algebra, 3rd Edition (Springer 2007), Field Theory, 2nd Edition (Springer 2005), and Introduction to the Mathematics of Finance (2004).

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 305
• Erscheinungstermin: 15. Dezember 2008
• Englisch
• ISBN-13: 9780387789019
• Artikelnr.: 37287972

Autorenporträt

Steven Roman, Ph.D., is a professor emeritus of mathematics at the California State University, Fullerton. His previous books with O'Reilly include Access Database Design and Programming, Writing Excel Macros, and Win32 API Programming with Visual Basic.

Inhaltsangabe

Preface.- 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.- Duality for Distributive Lattices: The Priestley Topology.- Free Lattices.- Fixed-Point Theorems.- Appendix A: A Bit of Topology.- Appendix B: A Bit of Category Theory.- References.- Index of Symbols.- Index.

Rezensionen

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)