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Author: Steven Givant
Publisher: Springer Science & Business Media
Published: 2008-12-10
Total Pages: 589
ISBN-13: 0387684360
DOWNLOAD EBOOKThis book is an informal though systematic series of lectures on Boolean algebras. It contains background chapters on topology and continuous functions and includes hundreds of exercises as well as a solutions manual.
Author: Paul R. Halmos
Publisher: Courier Dover Publications
Published: 2018-09-12
Total Pages: 163
ISBN-13: 0486834573
DOWNLOAD EBOOKThis presentation on the basics of Boolean algebra has ranked among the fundamental books on this important subject in mathematics and computing science since its initial publication in 1963. Concise and informal as well as systematic, the text draws upon lectures delivered by Professor Halmos at the University of Chicago to cover many topics in brief individual chapters. The approach is suitable for advanced undergraduates and graduate students in mathematics. Starting with Boolean rings and algebras, the treatment examines fields of sets, regular open sets, elementary relations, infinite operations, subalgebras, homomorphisms, free algebras, ideals and filters, and the homomorphism theorem. Additional topics include measure algebras, Boolean spaces, the representation theorem, duality for ideals and for homomorphisms, Boolean measure spaces, isomorphisms of factors, projective and injective algebras, and many other subjects. Several chapters conclude with stimulating exercises; the solutions are not included.
Author: Bradford Henry Arnold
Publisher: Courier Corporation
Published: 2011-01-01
Total Pages: 163
ISBN-13: 0486483851
DOWNLOAD EBOOKOrignally published: Englewood Cliffs, N.J.: Prentice-Hall, 1962.
Author: Frank Markham Brown
Publisher: Courier Corporation
Published: 2012-02-10
Total Pages: 308
ISBN-13: 0486164594
DOWNLOAD EBOOKConcise text begins with overview of elementary mathematical concepts and outlines theory of Boolean algebras; defines operators for elimination, division, and expansion; covers syllogistic reasoning, solution of Boolean equations, functional deduction. 1990 edition.
Author: Roman Sikorski
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 248
ISBN-13: 3642858201
DOWNLOAD EBOOKThere are two aspects to the theory of Boolean algebras; the algebraic and the set-theoretical. A Boolean algebra can be considered as a special kind of algebraic ring, or as a generalization of the set-theoretical notion of a field of sets. Fundamental theorems in both of these directions are due to M. H. STONE, whose papers have opened a new era in the develop ment of this theory. This work treats the set-theoretical aspect, with little mention being made of the algebraic one. The book is composed of two chapters and an appendix. Chapter I is devoted to the study of Boolean algebras from the point of view of finite Boolean operations only; a greater part of its contents can be found in the books of BIRKHOFF [2J and HERMES [1]. Chapter II seems to be the first systematic study of Boolean algebras with infinite Boolean operations. To understand Chapters I and II it suffices only to know fundamental notions from general set theory and set-theoretical topology. No know ledge of lattice theory or of abstract algebra is presumed. Less familiar topological theorems are recalled, and only a few examples use more advanced topological means; but these may be omitted. All theorems in both chapters are given with full proofs.
Author: J. Donald Monk
Publisher: Springer Science & Business Media
Published: 2010-03-25
Total Pages: 308
ISBN-13: 3034603347
DOWNLOAD EBOOKThis text covers cardinal number valued functions defined for any Boolean algebra such as cellularity. It explores the behavior of these functions under algebraic operations such as products, free products, ultraproducts and their relationships to each other.
Author: Steven Givant
Publisher: Springer Science & Business Media
Published: 2008-12-02
Total Pages: 589
ISBN-13: 0387402934
DOWNLOAD EBOOKThis book is an informal though systematic series of lectures on Boolean algebras. It contains background chapters on topology and continuous functions and includes hundreds of exercises as well as a solutions manual.
Author: Khanna, Vijay K.
Publisher: Vikas Publishing House
Published: 2004-12
Total Pages: 172
ISBN-13: 9788125916536
DOWNLOAD EBOOKThis 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.
Author: Ranganathan Padmanabhan
Publisher: World Scientific
Published: 2008
Total Pages: 229
ISBN-13: 9812834540
DOWNLOAD EBOOKThe 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.
Author: Elliott Mendelson
Publisher: McGraw Hill Professional
Published: 1970-06-22
Total Pages: 226
ISBN-13: 9780070414600
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