Lattices and Ordered Sets (PDF)
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...
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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).
- Autor: Steven Roman
- 2008, 2009, 305 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 0387789014
- ISBN-13: 9780387789019
- Erscheinungsdatum: 15.12.2008
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- Dateiformat: PDF
- Grösse: 2.16 MB
- Ohne Kopierschutz
- Vorlesefunktion
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)
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