Lattices and Ordered Sets

Lattices and Ordered Sets
Author :
Publisher : Springer Science & Business Media
Total Pages : 307
Release :
ISBN-10 : 9780387789019
ISBN-13 : 0387789014
Rating : 4/5 (014 Downloads)

Book Synopsis Lattices and Ordered Sets by : Steven Roman

Download or read book Lattices and Ordered Sets written by Steven Roman and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Lattices and Ordered Sets Related Books

Lattices and Ordered Sets
Language: en
Pages: 307
Authors: Steven Roman
Categories: Mathematics
Type: BOOK - Published: 2008-12-15 - Publisher: Springer Science & Business Media

GET EBOOK

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 gra
Lattices and Ordered Algebraic Structures
Language: en
Pages: 311
Authors: T.S. Blyth
Categories: Mathematics
Type: BOOK - Published: 2005-04-18 - Publisher: Springer Science & Business Media

GET EBOOK

"The text can serve as an introduction to fundamentals in the respective areas from a residuated-maps perspective and with an eye on coordinatization. The histo
Introduction to Lattices and Order
Language: en
Pages: 316
Authors: B. A. Davey
Categories: Mathematics
Type: BOOK - Published: 2002-04-18 - Publisher: Cambridge University Press

GET EBOOK

This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive develo
Ordered Sets
Language: en
Pages: 391
Authors: Egbert Harzheim
Categories: Mathematics
Type: BOOK - Published: 2005-02-17 - Publisher: Springer Science & Business Media

GET EBOOK

The textbook literature on ordered sets is still rather limited. A lot of material is presented in this book that appears now for the first time in a textbook.
Ordered Sets
Language: en
Pages: 401
Authors: Bernd Schröder
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

GET EBOOK

An introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoret