J Austral Math Soc Ser A 49 pp24--42, 1990.

The Lattice of Completely Regular Semigroup Varieties

Francis Pastijn

Abstract

A completely regular semigroup is a semigroup which is a union of groups. The class CR of completely regular semigroups forms a variety. On the lattice L(CR) of completely regular semigroup varieties we define two closure operations which induce complete congruences. The consideration of a third complete congruence on L(CR) yields a subdirect decomposition of L(CR). Using these results we show that L(CR) is arguesian. This confirms the (tacit) conjecture that L(CR) is modular.

1980 AMS Subject Classification (1985 Revision): primary 20M05; secondary 20M07, 08B15

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Authors

Francis Pastijn

Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, Wisconsin 53233, U.S.A.