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.)


Zbl 0267.50018
Full Text: EuDML


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