radical theory of idempotent algebras; ternary operation; involuted semigroups; semiheaps; generalised heaps; heaps
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 to a radical-theoretic interpretation of the largest idempotent-separating congruence.
 Baer R.: Zür Einfuhrung des Scharbegriffs. J. Reine Angew. Math. 160 (1929), 199--207.
 Hoehnke H.-J.: Einige neue Resultate über abstrakte Halbgruppen
. Colloq. Math. 14 (1966), 329--349. MR 0185027
| Zbl 0196.29501
 Howie J.M.: The maximum idempotent separating congruence on an inverse semigroup
. Proc. Edinburgh Math. Soc. 14 (1964/65), 71--79. MR 0163976
 Munn W.D.: Fundamental Inverse Semigroups
. Quart. J. Math. Oxford Ser. (2) 17 (1966), 157--170. MR 0262402
| Zbl 0219.20047
 Vagner V.V.: The theory of generalized heaps and generalized groups
. (Russian), Mat. Sbornik N.S. 32 (1953), 545--632. MR 0059267