Some quasigroup identities which are invariant by isotopy of quasigroups. (Russian) Zbl 0653.20071

Monosova, G.

Mat. Issled. 102, 80-91 (1988).

An identity of the form \(A_ 1(x_ 1,A_ 2(x_ 2,...,A_ n(x_ n,x_{n+1})...))=x_{n+2}\) (where all \(A_ i\) are quasigroups on the same set) is called canonical. The author shows that from several kinds of identities (e.g. from an identity which has length not more than 7) one can make a canonical identity with parastrophies. The paper contains also the definition of so called universal identities and some statements about their properties.

Reviewer: M.Csikós

MSC:

20N05

Loops, quasigroups

Keywords:

quasigroups; identities; parastrophies; universal identities