Subspaces and parallelity in semiaffine partial linear spaces
type: Item
instance of: scholarly article
title: Subspaces and parallelity in semiaffine partial linear spaces
zbMATH Open document ID: 1045.51001
DOI: 10.1007/BF02941272
author: D. Massart
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 2004-05-18T00:00:00Z
review text: The notion of semiaffine partial linear space was introduced by \textit{K. Radziszewski} [Zesz. Nauk., Geom. 19, 67--80 (1991; Zbl 0746.51003)]. The basic examples of these semiaffine partial linear spaces arise from cylinders over ruled quadrics, with generators of an arbitrary dimension. But there exist many other examples. The author studies in this article various properties of these semiaffine partial linear spaces. He characterizes subspaces and strong subspaces, considers the definability of projective and semiaffine planes, affine lines and parallelity in terms of projective lines. He also gives a construction of a wide class of semiaffine partial linear spaces.
Mathematics Subject Classification ID: 51A15
zbMATH DE Number: 2063939
zbMATH Keywords: semiaffine partial linear space
zbMATH Keywords: strong subspace
zbMATH Keywords: parallelity
reviewed by: Leo Storme
MaRDI profile type: Publication
cites work: Q4039891
cites work: Direct products of affine partial linear spaces
cites work: Bericht über geschlitzte Inzidenzgruppen
cites work: Q3980491
cites work: Q3980494
cites work: Q4546169
cites work: Affine partial line spaces
Recommended article: Q4206039
Recommended article: Q3980494
Recommended article: Affine partial line spaces
Recommended article: Semilinear spaces and their remarkable subsets
Recommended article: Generalized semiaffine linear spaces
Recommended article: Finite semiaffine linear spaces
Recommended article: PARTIAL LINEAR SPACES WITH DUAL AFFINE PLANES
Recommended article: Hyperstructures and linear spaces with parallelism
Recommended article: Q4032397
Recommended article: On decomposability of affine partial linear spaces
description: scientific article; zbMATH DE number 2063939