On the Grassmann space representing the lines of an affine space

AbstractIn 1982, Bichara and Mazzocca characterized the Grassmann space Gr(1,A) of the lines of an affine space A of dimension at least 3 over a skew-field K by means of the intersection properties of the three disjoint families Σ1,Σ2 and T of maximal singular subspaces of Gr(1,A). In this paper, we deal with the characterization of Gr(1,A) using only the family Σ=Σ1∪Σ2 of maximal singular subspaces

On the Grassmann space representing the lines of an affine space

In 1982 Bichara and Mazzocca characterized the Grassmann space Gr(1,A) of the lines of an affine space A of dimension at least 3 by means of the intersection properties of the three disjoint families S, S' and T of maximal singular subspaces of Gr(1,A). In this paper we deal with the characterization of Gr(1,A) using only the families S and S' of maximal singular subspaces