engleski

A class of quasigroups associated with a cubic Pisot number

In this paper idempotent medial quasigroups satisfying the identity (ab.a)a=b are studied. An example are the complex numbers with multiplication defined by a.b=(1-q)a+qb, where q is a solution of q^3-2q^2+q-1=0. The positive root of this cubic equation can be viewed as a generalization of the golden ratio. It turns out that the quasigroups under consideration have many similar properties to the so-called golden section quasigroups.

IM-quasigroup; Pisot number

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