Axioms for Lattices and Boolean Algebras

Axioms for Lattices and Boolean Algebras PDF

Author: Ranganathan Padmanabhan

Publisher: World Scientific

Published: 2008

Total Pages: 229

ISBN-13: 9812834540

DOWNLOAD EBOOK →

The importance of equational axioms emerged initially with the axiomatic approach to Boolean algebras, groups, and rings, and later in lattices. This unique research monograph systematically presents minimal equational axiom-systems for various lattice-related algebras, regardless of whether they are given in terms of ?join and meet? or other types of operations such as ternary operations. Each of the axiom-systems is coded in a handy way so that it is easy to follow the natural connection among the various axioms and to understand how to combine them to form new axiom systems. A new topic in this book is the characterization of Boolean algebras within the class of all uniquely complemented lattices. Here, the celebrated problem of E V Huntington is addressed, which ? according to G Gratzer, a leading expert in modern lattice theory ? is one of the two problems that shaped a century of research in lattice theory. Among other things, it is shown that there are infinitely many non-modular lattice identities that force a uniquely complemented lattice to be Boolean, thus providing several new axiom systems for Boolean algebras within the class of all uniquely complemented lattices. Finally, a few related lines of research are sketched, in the form of appendices, including one by Dr Willian McCune of the University of New Mexico, on applications of modern theorem-proving to the equational theory of lattices.

Lattices & Boolean Algebras: First Concepts

Lattices & Boolean Algebras: First Concepts PDF

Author: Khanna, Vijay K.

Publisher: Vikas Publishing House

Published: 2004-12

Total Pages: 166

ISBN-13: 8125916539

DOWNLOAD EBOOK →

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 with Unique Complements

Lattices with Unique Complements PDF

Author: Vi_acheslav Nikolaevich Sali_

Publisher: American Mathematical Soc.

Published: 1988-12-31

Total Pages: 132

ISBN-13: 9780821898178

DOWNLOAD EBOOK →

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.

Boolean Algebra Essentials

Boolean Algebra Essentials PDF

Author: Alan Solomon

Publisher: Research & Education Assoc.

Published: 2013-01-01

Total Pages: 116

ISBN-13: 9780738671673

DOWNLOAD EBOOK →

REA’s Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Boolean Algebra includes set theory, sentential calculus, fundamental ideas of Boolean algebras, lattices, rings and Boolean algebras, the structure of a Boolean algebra, and Boolean algebra in communication systems.

Ordered Sets and Lattices II

Ordered Sets and Lattices II PDF

Author:

Publisher: American Mathematical Soc.

Published:

Total Pages: 262

ISBN-13: 9780821895887

DOWNLOAD EBOOK →

This indispensable reference source contains a wealth of information on lattice theory. The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed in Referativnyi Zhurnal Matematika from mid-1982 to the end of 1985. A continuation of a previous volume (the English translation of which was published by the AMS in 1989, as volume 141 in Translations - Series 2), this comprehensive work contains more than 2200 references. Many of the papers covered here were originally published in virtually inaccessible places. The compilation of the volume was directed by Milan Kolibiar of Comenius University at Bratislava and Lev A. Skornyakov of Moscow University. Of interest to mathematicians, as well as to philosophers and computer scientists in certain areas, this unique compendium is a must for any mathematical library.

Abstract Algebra

Abstract Algebra PDF

Author: Thomas Judson

Publisher: Orthogonal Publishing L3c

Published: 2023-08-11

Total Pages: 0

ISBN-13: 9781944325190

DOWNLOAD EBOOK →

Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.

Modern Algebra

Modern Algebra PDF

Author: John R. Durbin

Publisher: John Wiley & Sons

Published: 2008-12-31

Total Pages: 354

ISBN-13: 0470384433

DOWNLOAD EBOOK →

Engineers and computer scientists who need a basic understanding of algebra will benefit from this accessible book. The sixth edition includes many carefully worked examples and proofs to guide them through abstract algebra successfully. It introduces the most important kinds of algebraic structures, and helps them improve their ability to understand and work with abstract ideas. New and revised exercise sets are integrated throughout the first four chapters. A more in-depth discussion is also included on Galois Theory. The first six chapters provide engineers and computer scientists with the core of the subject and then the book explores the concepts in more detail.

Introduction to Lattices and Order

Introduction to Lattices and Order PDF

Author: B. A. Davey

Publisher: Cambridge University Press

Published: 2002-04-18

Total Pages: 316

ISBN-13: 1107717523

DOWNLOAD EBOOK →

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.

Lanterna Rally - Theme by Grace Themes