Varieties of Structurally Trivial Semigroups III

The skeleton of the lattice of all structurally trivial semigroup varieties is known to be isomorphic to an infinitely ascending inverted pyramid (Kopamu, 2003 Kopamu , S. J. L. ( 2003 ). Varieties of structurally trivial semigroups II . Semigroup Forum 66 : 401 – 415 . [Google Scholar]). We digitize the skeleton by representing each variety forming the skeleton as an ordered triple of non-negative integers. This digitization of the lattice, under the pointwise ordering of non-negative integers, provides useful algorithms which could easily be programmed into a computer, and then used to compute varietal joins and meets, or even to draw skeleton lattice diagrams. An application to a certain larger subvariety lattice is also given as an example.