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SM ISO690:2012 KINYON, Michael, KRAPEZ, Aleksandar, PHILLIPS, Jon D.. Right product quasigroups and loops. In: Quasigroups and Related Systems, 2011, vol. 19, nr. 2(26), pp. 239-264. ISSN 1561-2848. |
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Quasigroups and Related Systems | ||||||
Volumul 19, Numărul 2(26) / 2011 / ISSN 1561-2848 | ||||||
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Pag. 239-264 | ||||||
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Right groups are direct products of right zero semigroups and groups and they play a signicant role in the semilattice decomposition theory of semigroups. Right groups can be characterized as associative right quasigroups (magmas in which left translations are bijective). If we do not assume associativity we get right quasigroups which are not
necessarily representable as direct products of right zero semigroups and quasigroups. To obtain such a representation, we need stronger assumptions which lead us to the notion
of right product quasigroup. If the quasigroup component is a (one-sided) loop, then we have a right product (left, right) loop. We nd a system of identities which axiomatizes right product quasigroups, and use this to nd axiom systems for right product (left, right) loops; in fact, we can obtain each
of the latter by adjoining just one appropriate axiom to the right product quasigroup axiom system. We derive other properties of right product quasigroups and loops, and conclude by showing that the axioms for right product quasigroups are independent. |
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Cuvinte-cheie right quasigroup, right product quasigroup, right product loop, axiomatization, axiom independence |
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