Lattices & Boolean Algebras: First Concepts
Title | Lattices & Boolean Algebras: First Concepts PDF eBook |
Author | Khanna, Vijay K. |
Publisher | Vikas Publishing House |
Pages | 172 |
Release | 2004-12 |
Genre | Mathematics |
ISBN | 9788125916536 |
This book is primarily designed for senior UG students wishing to pursue a course in Lattices/ Boolean Algebra, and those desirous of using lattice-theoretic concepts in their higher studies. Theoretical discussions amply illustrated by numerous examples and worked-out problems. Hints and solutions to select exercises added to the text as further help.
Lattices and Boolean Algebras
Title | Lattices and Boolean Algebras PDF eBook |
Author | V. K. Khanna |
Publisher | |
Pages | 148 |
Release | 1994 |
Genre | Lattice theory |
ISBN | 9780706983692 |
Lattice Theory
Title | Lattice Theory PDF eBook |
Author | George Gratzer |
Publisher | Courier Corporation |
Pages | 242 |
Release | 2009-01-01 |
Genre | Mathematics |
ISBN | 048647173X |
This outstanding text is written in clear language and enhanced with many exercises, diagrams, and proofs. It discusses historical developments and future directions and provides an extensive bibliography and references. 1971 edition.
Lattices and Boolean Algebra
Title | Lattices and Boolean Algebra PDF eBook |
Author | Vijay K. Khanna |
Publisher | |
Pages | 148 |
Release | 1994 |
Genre | |
ISBN |
Lattices and Ordered Sets
Title | Lattices and Ordered Sets PDF eBook |
Author | Steven Roman |
Publisher | Springer Science & Business Media |
Pages | 307 |
Release | 2008-12-15 |
Genre | Mathematics |
ISBN | 0387789014 |
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.
Introduction to Lattices and Order
Title | Introduction to Lattices and Order PDF eBook |
Author | B. A. Davey |
Publisher | Cambridge University Press |
Pages | 316 |
Release | 2002-04-18 |
Genre | Mathematics |
ISBN | 9780521784511 |
This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures.
Lattices with Unique Complements
Title | Lattices with Unique Complements PDF eBook |
Author | Vi_acheslav Nikolaevich Sali_ |
Publisher | American Mathematical Soc. |
Pages | 132 |
Release | 1988-12-31 |
Genre | Mathematics |
ISBN | 9780821898178 |
The class of uniquely complemented lattices properly contains all Boolean lattices. However, no explicit example of a non-Boolean lattice of this class has been found. In addition, the question of whether this class contains any complete non-Boolean lattices remains unanswered. This book focuses on these classical problems of lattice theory and the various attempts to solve them. Requiring no specialized knowledge, the book is directed at researchers and students interested in general algebra and mathematical logic.