J Austral Math Soc Ser A 55 pp270--286, 1993.

Hyperidentity Bases for Rectangular Bands and other Semigroup Varieties

Shelly L. Wismath

Abstract

Hyperidentities were introduced by Taylor, and their properties have been studied by Taylor, Bergman, Penner, Graczynska, Schweigert, Wismath and others. In particular, Penner has produced bases for the hyperidentities of various types satisfied by the variety of semilattices. In this paper, we look at bases for the hyperidentities satisfied by some other varieties of semigroups. We first investigate solid and hyper-associative varieties of semigroups, and use a result of Gracynska's to form a basis for the hyperidentities of type á2ñ for varieties with these properties. We then produce bases for the hyperidentities satisfied by the variety RB of rectangular bands, and prove that the collection of all hyperidentities satisfied by RB is not finitely based. Finally, we use the RB results to give hyperidentity bases for some varieties of nilpotent semigroups.

1991 AMS Subject Classification: 20M08

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Authors

Shelly L. Wismath

Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, Canada T1K 3M4.