Abstract
Infinite Steiner quasigroups, that is, commutative idempotent groupoids satisfying the identity (xy)x=y, form an almost universal category. As a consequence, every monoid is representable by all nonconstant endomorphisms of a Steiner quasi-group, and there is a proper class of nonisomorphic representations of this kind. Similar results are obtained for partial Steiner quasigroups as well as for partial and complete Steiner triple systems naturally corresponding to these algebras.
The support of the NSERC is gratefully acknowledged.
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© 1985 Springer-Verlag
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Pigozzi, D., Sichler, J. (1985). Homomorphisms of partial and of complete steiner triple systems and quasigroups. In: Comer, S.D. (eds) Universal Algebra and Lattice Theory. Lecture Notes in Mathematics, vol 1149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098467
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DOI: https://doi.org/10.1007/BFb0098467
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