Projective mappings between projective lattice geometries
type: Item
instance of: scholarly article
title: Projective mappings between projective lattice geometries
zbMATH Open document ID: 0847.51002
DOI: 10.1007/BF01222858
author: Thorsten Pfeiffer
author: Stefan E. Schmidt
published in: Journal of Geometry
publication date: 1996-10-15T00:00:00Z
review text: 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.
reviewed by: Hans Havlicek
Mathematics Subject Classification ID: 51A10
Mathematics Subject Classification ID: 51A05
Mathematics Subject Classification ID: 06B99
zbMATH DE Number: 827395
zbMATH Keywords: projective mapping
zbMATH Keywords: lattice geometry
zbMATH Keywords: residuation theory
MaRDI profile type: Publication
cites work: Q4056047
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full work available at URL: https://doi.org/10.1007/bf01222858
OpenAlex ID: W2081696354
description: scientific article; zbMATH DE number 827395