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Semiheaps are ternary generalisations of involuted semigroups. The first kind of semiheaps studied were heaps, which correspond closely to groups. We apply the radical theory of varieties of idempotent algebras to varieties of idempotent semiheaps. The class of heaps is shown to be a radical class, as are two larger classes having no involuted semigroup counterparts. Radical decompositions of various classes of idempotent semiheaps are given. The results are applied to involuted I-semigroups, leading...
Completely regular semigroups are considered here with the unary operation of inversion within the maximal subgroups of the semigroup. This makes a variety; its lattice of subvarieties is denoted by . We study here the relations and relative to a sublattice of constructed in a previous publication. For being any of these relations, we determine the -classes of all varieties in the lattice as well as the restrictions of to .
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