International Journal of Algebra
Semigroups, Varieties, Rees-Sushkevich, Permutative
A semigroup variety is a Rees–Sushkevich variety if it is contained in a periodic variety generated by 0-simple semigroups. The collection of all permutative combinatorial Rees–Sushkevich varieties constitutes an incomplete lattice that does not contain the complete join J of all its varieties. The objective of this article is to investigate the subvarieties of J. It is shown that J is locally finite, non-finitely generated, and contains only finitely based subvarieties. The subvarieties of J are precisely the combinatorial Rees–Sushkevich varieties that do not contain a certain semigroup of order four.
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Lee, Edmond W. H., "On the Complete Join of Permutative Combinatorial Rees–Sushkevich Varieties" (2007). Mathematics Faculty Articles. 139.