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Title: One configurational characterization of Ostrom nets (English)
Author: Baštinec, Jaromír
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 116
Issue: 2
Year: 1991
Pages: 132-147
Summary lang: English
Category: math
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. (English)
Keyword: net
Keyword: Ostrom net
Keyword: quadrilateral closure condition
Keyword: skew field
Keyword: quadrangular condition
MSC: 51A20
MSC: 51A25
idZBL: Zbl 0737.51002
idMR: MR1111998
DOI: 10.21136/MB.1991.126140
Date available: 2009-09-24T20:44:09Z
Last updated: 2020-07-29
Stable URL:
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Reference: [2b] V. Havel: General nets and their associated groupoids.Prac. Symp. "n-ary Structures", Skopje 1972, 229-241. MR 0735655
Reference: [3] J. Kadleček: Closure conditions in the nets.Comm. Math. Univ. Car. 19 (1978), 119-133. MR 0492374
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Reference: [5] H. Thiele: Gewebe, deren Ternärkörper aus einem Vektorraum hervorgeht.Mitt. Math. Sem. Giessen, Nr. 140 (1979), 32-79. Zbl 0406.51002, MR 0542564


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