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Axioms for lattices and boolean algebras /
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 ar...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, N.J. :
World Scientific Pub. Co.,
©2008.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Padmanabhan, R. |q (Ranganathan), |d 1938- | |
| 245 | 1 | 0 | |a Axioms for lattices and boolean algebras / |c R. Padmanabhan, S. Rudeanu. |
| 260 | |a Singapore ; |a Hackensack, N.J. : |b World Scientific Pub. Co., |c ©2008. | ||
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references (pages 193-210) and index. | ||
| 505 | 0 | |a 1. Semilattices and lattices -- 2. Modular lattices -- 3. Distributive lattices -- 4. Boolean algebras -- 5. Further topics and open problems. | |
| 520 | |a 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. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Lattice theory. | |
| 650 | 0 | |a Algebra, Boolean. | |
| 650 | 0 | |a Axioms. | |
| 650 | 6 | |a Théorie des treillis. | |
| 650 | 6 | |a Algèbre de Boole. | |
| 650 | 6 | |a Axiomes. | |
| 650 | 7 | |a MATHEMATICS |x Infinity. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Logic. |2 bisacsh | |
| 650 | 7 | |a Algebra, Boolean |2 fast | |
| 650 | 7 | |a Axioms |2 fast | |
| 650 | 7 | |a Lattice theory |2 fast | |
| 700 | 1 | |a Rudeanu, Sergiu. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521196 |z Texto completo |
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