Axioms For Lattices And Boolean Algebras

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Title:	Axioms For Lattices And Boolean Algebras
Description:	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.
Authors:	R Padmanabhan, Sergiu Rudeanu
Resource Type:	eBook.
Subjects:	Axioms, Lattice theory, Algebra, Boolean
Categories:	MATHEMATICS / Number Theory, COMPUTERS / Artificial Intelligence / General, MATHEMATICS / Logic
Database:	eBook Collection (EBSCOhost)

FullText	Links: – Type: ebook-pdf Text: Availability: 0
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Items	– Name: Title Label: Title Group: Ti Data: Axioms For Lattices And Boolean Algebras – Name: Abstract Label: Description Group: Ab Data: 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. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22R+Padmanabhan%22">R Padmanabhan</searchLink><br /><searchLink fieldCode="AR" term="%22Sergiu+Rudeanu%22">Sergiu Rudeanu</searchLink> – Name: TypePub Label: Resource Type Group: TypPub Data: eBook. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Axioms%22">Axioms</searchLink><br /><searchLink fieldCode="DE" term="%22Lattice+theory%22">Lattice theory</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%2C+Boolean%22">Algebra, Boolean</searchLink> – Name: SubjectBISAC Label: Categories Group: Su Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Number+Theory%22">MATHEMATICS / Number Theory</searchLink><br /><searchLink fieldCode="ZK" term="%22COMPUTERS+%2F+Artificial+Intelligence+%2F+General%22">COMPUTERS / Artificial Intelligence / General</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Logic%22">MATHEMATICS / Logic</searchLink>
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RecordInfo	BibRecord: BibEntity: Classifications: – Code: 511.33 Scheme: ddc Type: prePub Languages: – Code: eng Text: English Subjects: – SubjectFull: Axioms Type: general – SubjectFull: Lattice theory Type: general – SubjectFull: Algebra, Boolean Type: general Titles: – TitleFull: Axioms For Lattices And Boolean Algebras Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: R Padmanabhan – PersonEntity: Name: NameFull: Sergiu Rudeanu – PersonEntity: Name: NameFull: R Padmanabhan – PersonEntity: Name: NameFull: Sergiu Rudeanu IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2008 – D: 04 M: 02 Type: profile Y: 2014 Identifiers: – Type: isbn-print Value: 9789812834546 – Type: isbn-electronic Value: 9789812834553 Titles: – TitleFull: Axioms For Lattices And Boolean Algebras Type: main
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