Hyperidentity bases for rectangular bands and other semigroup varieties. (English) Zbl 0816.20053

Wismath, Shelly L.

J. Aust. Math. Soc., Ser. A 55, No. 2, 270-286 (1993).

[In Houston J. Math. 10, No. 1, 81-108 (1991; Zbl 0537.06005)], P. Penner produced hyperidentity bases for the variety of all semilattices. In this paper, the author uses the notions of varietal basis-solidity and hyper-associativity to obtain results on hyperidentity bases for some other semigroup varieties. Using the idea of the accessibility of a variable by projection, a hyperidentity basis is obtained for the variety of all rectangular bands. It is shown that the collection of all hyperidentities satisfied by rectangular bands is not finitely based. Finally, hyperidentity bases are provided for some varieties of nilpotent semigroups.

Reviewer: G.Clarke (Melbourne)

MSC:

20M07

Varieties and pseudovarieties of semigroups

Keywords:

hyperidentity bases; hyper-associativity; semigroup varieties; accessibility; rectangular bands; varieties of nilpotent semigroups

Citations:

Zbl 0537.06005