A note on projective coordinate systems of modular lattices (Q1207034)

A notion of a projective \(J\)-coordinate system of a modular complete lattice \(L\) is introduced, where \(J\) is a given set of indices. Next, the author proves that there is a 1-1 correspondence between \(R\) and \(S\), where \(R\) is the family of all \(J\)-coordinate systems of \(L\), \(S\) is the family of all mappings from \(2^ I\backslash\{0\}\) into \(L\) inducing complete lattice embeddings from \(2^ I \backslash \{i\}\) into \(L\) for all \(i \in I\), \(L\) is a modular, complete, and upper continuous lattice, and finally, \(I,J\) are given sets satisfying conditions \(J \subseteq I\) and \(| I \backslash J |=2\).