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The Lattice of Equational Classes of Semigroups with Zero

Published online by Cambridge University Press:  20 November 2018

Evelyn Nelson
Evelyn Nelson*
Affiliation:
Mcmaster University, Hamilton, Ontario
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 4 , December 1971 , pp. 531 - 534
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Burris, S. and Nelson, E., Embedding the dual of ∏m in the lattice of equational classes of commutative semigroups, Proc. Amer. Math. Soc. (to appear).Google Scholar
2. Burris, S., Embedding the dual of ∏∞ in the lattice of equational classes of semigroups, Algebra Universalis (to appear).Google Scholar
3. Gerhard, J. A., The lattice of equational classes of idempotent semigroups, J. Algebra 15 (1970), 195-224.Google Scholar
4. Head, T. J., The varieties of commutative monoids, Nieuw Archief voor Wiskunde (3) XVI, (1968), 203-206.Google Scholar
5. Nelson, E., The lattice of equational classes of commutative semigroups, Canad. J. Math, (to appear).Google Scholar
6. Sachs, D., Identities in finite partition lattices, Proc. Amer. Math. Soc. 12 (1969), 944-945.Google Scholar