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...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore
World Scientific Pub. Co.
c2008
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| Subjects: | |
| Online Access: | FHN01 Volltext |
| Summary: | 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 |
| Physical Description: | xi, 216 p. ill |
| ISBN: | 9789812834553 |
Staff View
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| id | DE-604.BV044637047 |
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| institution | BVB |
| isbn | 9789812834553 |
| language | English |
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| physical | xi, 216 p. ill |
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| spelling | Padmanabhan, R. 1938- Verfasser aut Axioms for lattices and boolean algebras R. Padmanabhan, S. Rudeanu Singapore World Scientific Pub. Co. c2008 xi, 216 p. ill txt rdacontent c rdamedia cr rdacarrier 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 Lattice theory Algebra, Boolean Axioms Rudeanu, Sergiu Sonstige oth http://www.worldscientific.com/worldscibooks/10.1142/7007#t=toc Verlag URL des Erstveroeffentlichers Volltext |
| spellingShingle | Padmanabhan, R. 1938- Axioms for lattices and boolean algebras Lattice theory Algebra, Boolean Axioms |
| title | Axioms for lattices and boolean algebras |
| title_auth | Axioms for lattices and boolean algebras |
| title_exact_search | Axioms for lattices and boolean algebras |
| title_full | Axioms for lattices and boolean algebras R. Padmanabhan, S. Rudeanu |
| title_fullStr | Axioms for lattices and boolean algebras R. Padmanabhan, S. Rudeanu |
| title_full_unstemmed | Axioms for lattices and boolean algebras R. Padmanabhan, S. Rudeanu |
| title_short | Axioms for lattices and boolean algebras |
| title_sort | axioms for lattices and boolean algebras |
| topic | Lattice theory Algebra, Boolean Axioms |
| topic_facet | Lattice theory Algebra, Boolean Axioms |
| url | http://www.worldscientific.com/worldscibooks/10.1142/7007#t=toc |
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