Abstract: This chapter presents the definition of the relation of partial order and then partially ordered sets, including chains. It presents two definitions of a lattice. The two definitions of lattice are proved equivalent and a number of examples of lattices are given. A lattice can be looked at in two distinct ways—from the point of view of either algebra or set theory. This is the reason why the applications of lattice theory are so remarkably widespread in other branches of mathematics and in the cognate sciences. A lattice is a partially ordered set in which every pair of elements possesses a greatest lower bound and a least upper bound within the set. Defining a lattice in algebraic terms proved that every lattice is a partially ordered set with special properties.
Publication Year: 1968
Publication Date: 1968-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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