Varieties of Structurally Trivial Semigroups III

Abstract

The skeleton of the lattice of all structurally trivial semigroup varieties is known to be isomorphic to an infinitely ascending inverted pyramid (Kopamu, 2003). 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.

Key Words:

• Lattices
• Semigroups
• Structurally-trivial
• Varieties

AMS 2000 Mathematics Subject Classification:

• 20M07

ACKNOWLEDGMENT

The author wishes to thank the editor and the anonymous referee for their comments and corrections which greatly improved the exposition of the article.

Notes

Communicated by D. Easdown.