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Radical decompositions of semiheaps

Ian Hawthorn, Tim Stokes (2009)

Commentationes Mathematicae Universitatis Carolinae

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...

Representation of involuted semigroups by binary relations

B. Schein (1974)

Fundamenta Mathematicae

Subtractive groupoids and laterally commutative heaps

Volenec, Vladimir (1990)

Portugaliae mathematica

Ternary halfgroupoids and coordinatization

Václav Havel (1969)

Matematický časopis

Ternary rings associated to translation plane

Josef Klouda (1977)

Commentationes Mathematicae Universitatis Carolinae

Ternary semigroups of morphisms of objects in categories

Antoni Chronowski, Miroslav Novotný (1995)

Archivum Mathematicum

In this paper the notion of a ternary semigroup of morphisms of objects in a category is introduced. The connection between an isomorphism of categories and an isomorphism of ternary semigroups of morphisms of suitable objects in these categories is considered. Finally, the results obtained for general categories are applied to the categories $𝐑𝐄𝐋 n + 1$ and $𝐀𝐋𝐆 n$ which were studied in [5].