Translations of Mathematical Monographs 1988; 113 pp; hardcover Volume: 69 ISBN10: 0821845225 ISBN13: 9780821845226 List Price: US$55 Member Price: US$44 Order Code: MMONO/69
 The class of uniquely complemented lattices properly contains all Boolean lattices. However, no explicit example of a nonBoolean lattice of this class has been found. In addition, the question of whether this class contains any complete nonBoolean lattices remains unanswered. This book focuses on these classical problems of lattice theory and the various attempts to solve them. Requiring no specialized knowledge, the book is directed at researchers and students interested in general algebra and mathematical logic. Table of Contents  Ordered sets
 Lattices
 Modular lattices
 Distributive lattices
 Complemented lattices
 Boolean algebras
 Axiomatics of Boolean algebras
 Do there exist nondistributive uniquely complemented lattices?
 There exist nondistributive uniquely complemented lattices
 Complete lattices
 Completion by cuts
 Representations of complete lattices
 Algebraic lattices
 Continuous lattices
 Collectively complemented lattices
 Orthogonal systems and lattice transformations of sets
 Regular elements and decomposition theorems for complete uniquely complemented lattices
