Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493417 | Journal of Algebra | 2005 | 35 Pages |
Abstract
The problem of the existence of non-medial distributive hamiltonian quasigroups is solved. Translating this problem first to commutative Moufang loops with operators, then to ternary algebras and, finally, to cocyclic modules over Z[x,xâ1,(1âx)â1], it is shown that every non-medial distributive hamiltonian quasigroup has at least 729 elements and that there are just two isomorphism classes of such quasigroups of the least cardinality. The quasigroups representing these two classes are anti-isomorphic.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Dolors Herbera, TomáÅ¡ Kepka, Petr NÄmec,