On the existence of special quasifields
This note is devoted to the construction of planar quasifields \((Q,+,\cdot)\) having the following special properties: Q is formally- real, it admits an ordering the natural place ring of which is not invariant, the rational numbers lie in the centre of Q, and the rule \((- x)y=-(xy)\) does not hold in Q. In view of the latter properties, a question of \textit{H. Wähling} [Theorie der Fastkörper (Essen 1987; Zbl 0669.12014), problem 2, p. 14] is answered in the negative.
scientific article; zbMATH DE number 4191840
scientific article