Axioms For Lattices And Boolean Algebras
Seiten
2008
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-283-454-6 (ISBN)
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-283-454-6 (ISBN)
- Titel z.Zt. nicht lieferbar
- Versandkostenfrei
- Auch auf Rechnung
- Artikel merken
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.
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.
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.
Equational Axiom Systems for Semilattices, Lattices, Modular and Distributive Lattices, and Boolean Algebras; New Huntington Varieties (= Defined by Lattice Identities Characterizing Boolean Algebras Among the Class of All Uniquely Complemented Lattices); Minimal Self-Dual Axiom Systems for Lattices and Boolean Algebras, Discovering New Axioms with the Aid of Modern Theorem-Provers.
| Erscheint lt. Verlag | 12.8.2008 |
|---|---|
| Verlagsort | Singapore |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre |
| ISBN-10 | 981-283-454-0 / 9812834540 |
| ISBN-13 | 978-981-283-454-6 / 9789812834546 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Buch | Softcover (2024)
World Scientific Publishing Co Pte Ltd (Verlag)
CHF 43,60
what we have that machines don't
Buch | Softcover (2024)
Profile Books Ltd (Verlag)
CHF 19,15
how simple questions lead us to mathematics’ deepest truths
Buch | Softcover (2024)
Profile Books Ltd (Verlag)
CHF 19,15
