Ternary Rings of a Class of Linearly Representable Semi-Translation Planes,

摘要

The theory of linear representation of projective planes was developed by Bruck and one of the authors (Bose) in two earlier papers (1964) and (1966),respectively. Bose and Barlotti obtained some new linear representations by generating the concept of incidence in the representation. In this paper,it is shown that the delta-planes of Bose and Barlotti are semi-translation planes,and the ternary rings of these planes are obtained,where the ternary function of delta is expressed explicitly in terms of the addition and multiplication in the Veblen-Wedderburn system, coordinatizing the translation plane T,from which delta can be obtained by dualization and derivation. (Author)