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The Lattice of Equational Classes of Commutative Semigroups

Published online by Cambridge University Press:  20 November 2018

Evelyn Nelson
Evelyn Nelson*
Affiliation:
McMaster University, Hamilton, Ontario
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There has been some interest lately in equational classes of commutative semigroups (see, for example, [2; 4; 7; 8]). The atoms of the lattice of equational classes of commutative semigroups have been known for some time [5]. Perkins [6] has shown that each equational class of commutative semigroups is finitely based. Recently, Schwabauer [7; 8] proved that the lattice is not modular, and described a distributive sublattice of the lattice.

The present paper describes a “skeleton” sublattice of the lattice, which is isomorphic to A × N+ with a unit adjoined, where A is the lattice of pairs (r, s) of non-negative integers with r ≦ s and s ≧ 1, ordered component-wise, and N+ is the natural numbers with division.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 5 , October 1971 , pp. 875 - 895
Copyright
Copyright © Canadian Mathematical Society 1971

Footnotes

This paper is a revision of the author's doctoral dissertation, written under the supervision of Dr. G. Bruns at McMaster University, Hamilton, Ontario.

References

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