The Lattice of Equational Classes of Semigroups with Zero
Evelyn M. Nelson · Canadian Mathematical Bulletin · 1971
In contrast to the very complicated structure of the lattice of equational classes of commutative semigroups (see [5]), the lattice of equational classes of commutative monoids (semigroups with unit) is isomorphic with N × N* with a unit adjoined, where N is the lattice of natural numbers with the usual order and N* is the lattice of natural numbers ordered by division. (See [4].) However, the lattice of equational classes of commutative semigroups-with-zero is not so simple to describe.