The Monoidal Interval for the Monoid Generated by Two Constants
In 1941, Post presented the complete description of the countably many clones on a 2-element set. The structure of the lattice of clones on sets of finitely many (but more than 2) elements is more complex; in fact, the lattice is of cardinality 2x0 . One approach is to study the monoidal intervals: the set of clones whose unary operations form a given monoid. In this article, we study the monoidal interval for the monoid generated by two constants on sets of k elements for k finite. This interval contains the clones of term operations of the bounded lattices of k elements.
Keywords: Universal algebra, clone, monoidal interval, distributive lattice.