# zbMATH — the first resource for mathematics

Quasigroups with completely reducible balanced identities. (Russian) Zbl 0587.20037
An identity $$W_ 1=W_ 2$$ is balanced if each variable appears exactly twice in the identity, once on each side. A balanced identity is reducible when the following conditions hold: If $$W_ 1$$ contains a subword xy then $$W_ 2$$ also contains xy or yx. If $$W_ 1=xu$$ or $$W_ 1=ux$$ then $$W_ 2=xv$$ or $$W_ 2=vx$$ (x and y are variables, u and v are subwords). Generalising this definition the author defines the quasigroups mentioned in the title. He proves that every completely reducible balanced identity falls into pieces of a system of such identities.
Reviewer: M.Csikós

##### MSC:
 20N05 Loops, quasigroups
##### Keywords:
quasigroups; completely reducible balanced identity
Full Text: