Projective mappings between projective lattice geometries
The authors discuss a class of structure-preserving mappings of projective lattice geometries [\textit{M. Greferath} and the second author, Geom. Dedicata 43, No. 3, 243-264 (1992; Zbl 0787.51004)] which they call projective mappings. On one hand the present investigation is based on residuation theory and on the other hand it is motivated by a characterization of ``linear mappings'' of (classical) projective spaces due to \textit{H. Brauner} [Monatsh. Math. 77, 10-20 (1973; Zbl 0256.50013)]; see also \textit{C. A. Faure} and \textit{A. Frölicher} [Geom. Dedicata 47, No. 1, 25-40 (1993; Zbl 0784.51003)]. It is striking to see that many of the classical results such as the characterization of projections as idempotent projective mappings and the homomorphism theorem remain true even in the very general framework of projective lattice geometry.
scientific article; zbMATH DE number 827395