Medial idempotent groupoids. II. (English) Zbl 0889.20043
Contributions to general algebra 9. Proceedings of the conference, Linz, Austria, June 1994. Wien: Hölder-Pichler-Tempsky, 133-150 (1995).
The main result of this second part [see Czech. Math. J. 41(116), No. 2, 249-259 (1991; Zbl 0738.20061) for the first one], is the following theorem: Let \(G\) be an idempotent medial groupoid. Then the number \(p_2(G)\) of essentially binary polynomials in \(G\) is 5 if and only if \(G\) is either a non-trivial affine space over \(\text{GF}(7)\) or a non-trivial Płonka sum of affine spaces over \(\text{GF}(5)\).
For the entire collection see [Zbl 0879.00039].
For the entire collection see [Zbl 0879.00039].
Reviewer: T.Kepka (Praha)
MSC:
| 20N02 | Sets with a single binary operation (groupoids) |
| 08A40 | Operations and polynomials in algebraic structures, primal algebras |
