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Biternärringe und affine lokale Ternärringe. (Biternary rings and affine local ternary rings). (German) Zbl 0693.51002

The author compares two classes of algebraic structures which are used to coordinate affine Klingenberg planes. The first class consists of the local ternary rings introduced by the author [Math. Slovaca 27, 181-193 (1977; Zbl 0359.50017)], and the second class contains the biternary rings defined by P. Y. Bacon [An Introduction to Klingenberg Planes. Vol. 1 (1976; Zbl 0372.50003)]. The author proves that these two sorts of structures are essentially equivalent by introducing an intermediate structure called an incomplete biternary ring.
Reviewer: N.Knarr

MSC:

51C05 Ring geometry (Hjelmslev, Barbilian, etc.)
51A25 Algebraization in linear incidence geometry
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References:

[1] Bacon P. Y.: An Introduction to Klingenberg Planes. Volume 1, Published by P. Y. Bacon 1976. · Zbl 0372.50003
[2] Machala F.: Erweiterte lokale Ternärringe. Czech. Math. J. 27 (102), 1977, 560-572. · Zbl 0391.17003
[3] Machala F.: Koordinatisation affiner Ebenen mit Homomorphismus. Math. Slovaca 27, No.2, 1977, 181-193. · Zbl 0359.50017
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