zbMATH — the first resource for mathematics

Coordinatization of projective planes by special planar ternary rings. (English) Zbl 0961.51003
The notion of an admissible planar ternary ring (APTR) is introduced by a slight modification of the well-known planar ternary rings found e.g. in [D. R. Hughes and F. C. Piper, ‘Projective planes’ (1973; Zbl 0267.50018)]. A number of existing theorems concerning geometrical properties (transitivity) of the plane and algebraic properties of a coordinatizing APTR are reformulated and reproved.

51C05 Ring geometry (Hjelmslev, Barbilian, etc.)
51A25 Algebraization in linear incidence geometry
20N10 Ternary systems (heaps, semiheaps, heapoids, etc.)
Full Text: EuDML
[1] Martin G. E.: Projective planes and isotopic ternary rings. Amer. Math. Monthly 74 (1967), 1185-1195. · Zbl 0164.51401 · doi:10.2307/2315659
[2] Martin G. E.: Projective planes and isogeic ternary rings. Estratto ”Le matematiche”, 23, 1 (1968), 185-196. · Zbl 0188.24404
[3] Klucky D.: Natural planar ternary rings. Acta Univ. Palacki. Olomuc., Fac. rer. nat., 69 (1981), 47-57. · Zbl 0483.51003 · eudml:23387
[4] Klucky D., Markova L.: Ternary rings with a left quasi-zero belonging to translation planes. Acta Univ. Palacki. Olomuc., Fac. rer. nat., 65 (1980), 89-100. · Zbl 0492.51002 · eudml:23372
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.