Sergiu Rudeanu's Books

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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Page Count

229

Publisher

World Scientific

Published Date

ISBN 10

9812834540

ISBN 13

9789812834546

Sets and Ordered Structures

By: Sergiu Rudeanu

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Sets and Ordered Structures

By: Sergiu Rudeanu

This e-book presents several basic methods and results of order theory that are currently used in various branches of mathematics. It presents topics that require a broad explanation in a concise and attractive way. Readers will easily identify problems/t

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Page Count

260

Publisher

Bentham Science Publishers

Published Date

ISBN 10

1608053385

ISBN 13

9781608053384

Lattice Functions and Equations

By: Sergiu Rudeanu

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Lattice Functions and Equations

By: Sergiu Rudeanu

One of the chief aims of this self-contained monograph is to survey recent developments of Boolean functions and equations, as well as lattice functions and equations in more general classes of lattices. Lattice (Boolean) functions are algebraic functions defined over an arbitrary lattice (Boolean algebra), while lattice (Boolean) equations are equations expressed in terms of lattice (Boolean) functions. Special attention is also paid to consistency conditions and reproductive general solutions. Applications refer to graph theory, automata theory, synthesis of circuits, fault detection, databases, marketing and others. Lattice Functions and Equations updates and extends the author's previous monograph - Boolean Functions and Equations.

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Page Count

442

Publisher

Springer Science & Business Media

Published Date

ISBN 10

144710241X

ISBN 13

9781447102410

Lattice Functions and Equations

By: Sergiu Rudeanu

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Lattice Functions and Equations

By: Sergiu Rudeanu

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Page Count

442

Publisher

Springer Science & Business Media

Published Date

ISBN 10

144710241X

ISBN 13

9781447102410

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

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Page Count

229

Publisher

World Scientific

Published Date

ISBN 10

9812834540

ISBN 13

9789812834546

Lung Cancer

Clinical and Surgical Specifications

By: Sergiu Rudeanu

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Lung Cancer

Clinical and Surgical Specifications

By: Sergiu Rudeanu

Lung cancer diagnosis worldwide has advanced considerably. Progress in diagnostic techniques and therapeutic methods has greatly improved life expectancy in lung cancer patients. Information on lung cancer diagnosis and treatment is therefore useful for

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Published Date

ISBN 10

1608054438

ISBN 13

9781608054435

Book's by Sergiu Rudeanu

Axioms for Lattices and Boolean Algebras

Axioms for Lattices and Boolean Algebras

Sets and Ordered Structures

Sets and Ordered Structures

Lattice Functions and Equations

Lattice Functions and Equations

Lattice Functions and Equations

Lattice Functions and Equations

Axioms for Lattices and Boolean Algebras

Axioms for Lattices and Boolean Algebras

Lung Cancer

Lung Cancer

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