Journal Title/Source
Quasigroups and Related Systems
Publication Date
2011
Volume
19
Page Numbers
239–264
Document Type
Journal Article
Department
Mathematics and Computer Science
Abstract
Right groups are direct products of right zero semigroups and groups and they play a significant 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 find a system of identities which axiomatizes right product quasigroups, and use this to find 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
Recommended Citation
Phillips, J.D., "Right product quasigroups and loops" (2011). Journal Articles. 515.
https://commons.nmu.edu/facwork_journalarticles/515