Thumbnail Image

General Method for the Construction of Free Lattice-ordered Algebras

McClurkan, Michael B.
A method for the construction of free lattice-ordered algebras was developed in the setting of a variety of abstract algebras in which subdirectly irreducible algebras are totally ordered. The method developed simplified the problem of construction of free t-algebras in that the free unordered algebra, which is in general easier to find, is used. Various examples of varieties of algebras for which this method of construction is valid were presented and noted as the motivating factors for this paper. One particular construction, that of a Boolean algebra, led me to be able to characterize the cardinality of finite free Boolean algebras. This characterization in turn led to a result that described the order of a free t-algebra in a somewhat more general setting.