Lattices And Boolean Algebras

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Lattices Boolean Algebras First Concepts

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Author : Khanna, Vijay K.
language : en
Publisher: Vikas Publishing House
Release Date : 2004-12

Lattices Boolean Algebras First Concepts written by Khanna, Vijay K. and has been published by Vikas Publishing House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12 with Mathematics categories.

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.

Axioms For Lattices And Boolean Algebras

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Author : Ranganathan Padmanabhan
language : en
Publisher: World Scientific
Release Date : 2008

Axioms For Lattices And Boolean Algebras written by Ranganathan Padmanabhan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

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.

Abstract Algebra

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Author : Thomas Judson
language : en
Publisher: Orthogonal Publishing L3c
Release Date : 2023-08-11

Abstract Algebra written by Thomas Judson and has been published by Orthogonal Publishing L3c this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-11 with categories.

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.

Axioms For Lattices And Boolean Algebras

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Author : Ranganathan Padmanabhan
language : en
Publisher: World Scientific
Release Date : 2008

Axioms For Lattices And Boolean Algebras written by Ranganathan Padmanabhan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Computers categories.

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 OC join and meetOCO 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 OCo according to G Gratzer, a leading expert in modern lattice theory OCo 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 And Ordered Algebraic Structures

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Author : T.S. Blyth
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-04-18

Lattices And Ordered Algebraic Structures written by T.S. Blyth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-18 with Mathematics categories.

"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 historical notes that are interspersed are also worth mentioning....The exposition is thorough and all proofs that the reviewer checked were highly polished....Overall, the book is a well-done introduction from a distinct point of view and with exposure to the author’s research expertise." --MATHEMATICAL REVIEWS

Sets Lattices And Boolean Algebras

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Author : James Crawford Abbott
language : en
Publisher:
Release Date : 1969

Sets Lattices And Boolean Algebras written by James Crawford Abbott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Algebra, Boolean categories.

Introduction To Boolean Algebras

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Author : Steven Givant
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10

Introduction To Boolean Algebras written by Steven Givant and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Mathematics categories.

This 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.

Lattices And Boolean Algebras

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Author : V. K. Khanna
language : en
Publisher:
Release Date : 1994

Lattices And Boolean Algebras written by V. K. Khanna and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Lattice theory categories.

Switching Theory For Logic Synthesis

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Author : Tsutomu Sasao
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Switching Theory For Logic Synthesis written by Tsutomu Sasao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.

Switching Theory for Logic Synthesis covers the basic topics of switching theory and logic synthesis in fourteen chapters. Chapters 1 through 5 provide the mathematical foundation. Chapters 6 through 8 include an introduction to sequential circuits, optimization of sequential machines and asynchronous sequential circuits. Chapters 9 through 14 are the main feature of the book. These chapters introduce and explain various topics that make up the subject of logic synthesis: multi-valued input two-valued output function, logic design for PLDs/FPGAs, EXOR-based design, and complexity theories of logic networks. An appendix providing a history of switching theory is included. The reference list consists of over four hundred entries. Switching Theory for Logic Synthesis is based on the author's lectures at Kyushu Institute of Technology as well as seminars for CAD engineers from various Japanese technology companies. Switching Theory for Logic Synthesis will be of interest to CAD professionals and students at the advanced level. It is also useful as a textbook, as each chapter contains examples, illustrations, and exercises.

Introduction To Lattices And Order

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Author : B. A. Davey
language : en
Publisher: Cambridge University Press
Release Date : 2002-04-18

Introduction To Lattices And Order written by B. A. Davey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-18 with Mathematics categories.

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.