Ranganathan Padmanabhan's Books

Axioms for Lattices and Boolean Algebras

By: Ranganathan Padmanabhan

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Axioms for Lattices and Boolean Algebras

By: Ranganathan Padmanabhan

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.

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Page Count

229

Publisher

World Scientific

Published Date

ISBN 10

9812834559

ISBN 13

9789812834553

Axioms for Lattices and Boolean Algebras

By: Ranganathan Padmanabhan,Sergiu Rudeanu

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Axioms for Lattices and Boolean Algebras

By: Ranganathan Padmanabhan,Sergiu Rudeanu

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.

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229

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World Scientific

Published Date

ISBN 10

9812834540

ISBN 13

9789812834546

Love is My Form: The advent (1926-1950)

By: Ranganathan Padmanaban

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Love is My Form: The advent (1926-1950)

By: Ranganathan Padmanaban

This Book, First Volume In The Series, Covers The First 25 Years In The Life Of Sri Sathya Sai Baba, Renowned World Teacher From India. It Follows Sai Baba As Sathya And Then As Raju, Through His Trials And Tribulations As A School Boy To His Declaration That He Was 'Sai Baba', The Saint Of Shirdi Reborn. By The Age Of 25 He Had Set Up An Ashram In The Remote Village Of His Birth, Calling It Prasanthi Nilayam That In The Following Years Became An International Pilgrimage Centre. Through Recorded Facts And Events, Interviews Of Contemporaries, Maps, Documents, Illustrations, Photographs And Letters, The Biographical Series, Aims To Document For Posterity The Life, The Works And The Teachings Of This Extraordinary Person.

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Sai Towers Publishing

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ISBN 10

8186822771

ISBN 13

9788186822777

Book's by Ranganathan Padmanabhan

Axioms for Lattices and Boolean Algebras

Axioms for Lattices and Boolean Algebras

Axioms for Lattices and Boolean Algebras

Axioms for Lattices and Boolean Algebras

Love is My Form: The advent (1926-1950)

Love is My Form: The advent (1926-1950)

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