Axioms For Lattices And Boolean Algebras

Ebook Details

Authors

R. Padmanabhan, S. Rudeanu

Year 2008
Pages 228
Publisher World Scientific Publishing Company
Language en
ISBN 9789812834546
File Size 1013.99 KB
File Format PDF
Download Counter 254
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Ebook Description

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.