The Resource Axioms for lattices and boolean algebras, R. Padmanabhan, S. Rudeanu

Axioms for lattices and boolean algebras, R. Padmanabhan, S. Rudeanu

Label
Axioms for lattices and boolean algebras
Title
Axioms for lattices and boolean algebras
Statement of responsibility
R. Padmanabhan, S. Rudeanu
Creator
Contributor
Subject
Language
eng
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
Cataloging source
LGG
Dewey number
511.3/3
Illustrations
illustrations
Index
index present
LC call number
QA171.5
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Label
Axioms for lattices and boolean algebras, R. Padmanabhan, S. Rudeanu
Publication
Bibliography note
Includes bibliographical references (p. 193-210) and index
http://library.link/vocab/branchCode
  • net
Color
multicolored
Contents
1. Semilattices and lattices -- 2. Modular lattices -- 3. Distributive lattices -- 4. Boolean algebras -- 5. Further topics and open problems
Control code
ocn820944613
Dimensions
unknown
Extent
1 online resource
Form of item
online
Isbn
9789812834553
http://library.link/vocab/recordID
.b32106622
Specific material designation
remote
System control number
  • (OCoLC)820944613
  • ebrary9812834559

Library Locations

    • Deakin University Library - Geelong Waurn Ponds CampusBorrow it
      75 Pigdons Road, Waurn Ponds, Victoria, 3216, AU
      -38.195656 144.304955
Processing Feedback ...