| Description |
1 online resource |
| Physical Medium |
polychrome |
| Description |
text file |
| Bibliography |
Includes bibliographical references (pages 193-210) and index. |
| Contents |
1. Semilattices and lattices -- 2. Modular lattices -- 3. Distributive lattices -- 4. Boolean algebras -- 5. Further topics and open problems. |
| 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. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Lattice theory.
|
|
Lattice theory. |
|
Algebra, Boolean.
|
|
Algebra, Boolean. |
|
Axioms.
|
|
Axioms. |
| Genre/Form |
Electronic books.
|
|
Electronic books.
|
| Added Author |
Rudeanu, Sergiu.
|
| ISBN |
9789812834553 (electronic book) |
|
9812834559 (electronic book) |
|
