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Keywords:
net; Ostrom net; quadrilateral closure condition; skew field; quadrangular condition
net; Ostrom net; quadrilateral closure condition; skew field; quadrangular condition
Summary:
Bz the quadrileteral condition in a given net there is meant the following implication: If $A_1, A_2, A_3,A-4$ are arbitrary points, no three of them lie on the same line, with coll $(A_iA_j)$ (collinearity) for any five from six couples $\{i,j\}$ then there follows the collinearity coll $(A_kA_l)$ for the remaining couple $\{k,l\}$.
In the article there is proved the every net satisfying the preceding configuration condition is necessarity the Ostrom net (i.e., the net over a field). Conversely, every Ostrom net satisfies the above configuration condition.
References:
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[1d] V. D. Belousov: Configurations in algebraic nets. (in Russian), Kishinev 1979. MR 0544665
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