Geodesic
The Lattice of Equational Classes of Semigroups with Zero
Canadian mathematical bulletin, Tome 14 (1971) no. 4, pp. 531-534

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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. 
Nelson, Evelyn. The Lattice of Equational Classes of Semigroups with Zero. Canadian mathematical bulletin, Tome 14 (1971) no. 4, pp. 531-534. doi: 10.4153/CMB-1971-094-3
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     title = {The {Lattice} of {Equational} {Classes} of {Semigroups} with {Zero}},
     journal = {Canadian mathematical bulletin},
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     year = {1971},
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     doi = {10.4153/CMB-1971-094-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-094-3/}
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