Affine planes over finite rings, a summary
type: Item
instance of: scholarly article
title: Affine planes over finite rings, a summary
zbMATH Open document ID: 1380.51006
published in: Aequationes Mathematicae
publication date: 2017-10-26T00:00:00Z
review text: The paper gives a state of art concerning affine planes over finite rings. An overview on Barbilian domains (introduced by \textit{W. Leissner} [J. Geom. 6, 31--57 (1975; Zbl 0296.50005)]) is given together with their main properties. Further, a survey on affine ring planes is given together with an overview of results characterizing affine Leissner, Klingenberg and Hjelmslev planes.
reviewed by: Gloria Rinaldi
Mathematics Subject Classification ID: 51C05
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 6798722
zbMATH Keywords: affine plane
zbMATH Keywords: ring geometry
zbMATH Keywords: Barbilian domain
zbMATH Keywords: Desarguesian plane
zbMATH Keywords: Hjelmslev plane
zbMATH Keywords: finite rings
author: Dirk Keppens
MaRDI profile type: Publication
full work available at URL: s00010-017-0497-4
OpenAlex ID: W2729448979
cites work: Q5628796
cites work: A way to the geometry of rings
cites work: Ratios of points in affine spaces over modules
cites work: Desarguesian Klingenberg Planes
cites work: Zur Axiomatik der projektiven ebenen Ringgeometrien. 1. Tl
cites work: Zur Axiomatik der projektiven ebenen Ringgeometrien. 2. Tl
cites work: Free cyclic submodules in the context of the projective line
cites work: Q4107139
cites work: Q4107555
cites work: \(\Omega\)-Geometrie und Geometrie von Hjelmslev. (\(\Omega\)-geometry and geometry of Hjelmslev)
cites work: Ebene Geometrie über einem Ring
cites work: On Barbilian domains over commutative rings
cites work: Q4548814
cites work: Q4505257
cites work: On hyperplanes and free subspaces of affine Klingenberg spaces
cites work: Subspace operations in affine Klingenberg spaces
cites work: The connected components on the projective line over a ring
cites work: Q4764138
cites work: Q3059731
cites work: On the structure of the \(GL_ 2\) of a ring
cites work: Q5639812
cites work: Q4764146
cites work: Q4776504
cites work: Projektive Geometrien mit Homomorphismus
cites work: Affine geometry of vector spaces over rings
cites work: Barbilian planes
cites work: The role of nonassociative algebra in projective geometry
cites work: Q3883080
cites work: Q3464679
cites work: Q5691167
cites work: 50 years of finite geometry
cites work: Projektive und affine Ebenen mit Nachbarelementen
cites work: Desarguessche Ebenen mit Nachbarelementen
cites work: Hjelmslev-Räume. (Hjelmslev spaces)
cites work: Free modules over Hjelmslev rings in which not every maximal linearly independent subset is a basis
cites work: Geometrical maps in ring affine geometries
cites work: Q2734153
cites work: Affine geometry of modules over a ring with an invariant basis number
cites work: Uniqueness of Barbilian domains
cites work: Affine Barbilian-Ebenen. I
cites work: Affine Barbilian-Ebenen. II
cites work: On classifying affine Barbilian spaces
cites work: Rings of stable rank 2 are Barbilian rings
cites work: Affine geometry over free unitary modules
cites work: Coordinate theorems for affine Hjelmslev planes
cites work: Q4087899
cites work: Q3797780
cites work: What is a Collineation of the Integer Plane?
cites work: Desarguesian affine Hjelmslev planes.
cites work: Projektive Hjelmslevräume.
cites work: Affine Hjelmslev-Ebenen mit transitiver Translationsgruppe
cites work: Faulkner geometry
cites work: Q3797779
cites work: Finite Rings with Applications
cites work: Pappian affine Klingenberg planes
cites work: Q5619454
cites work: Q5584442
cites work: Quantum entanglement and projective ring geometry
cites work: Affine Barbilian structures

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cites work: The coordinatization of affine planes by rings

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cites work: Fundamentalsatz für affine Räume über Moduln

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cites work: Der kleine Satz von Desargues in affinen Hjelmslev-Ebenen

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cites work: Literature on geometry over rings

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cites work: Q4764155

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cites work: \(n\)-Barbilian domains

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cites work: Q4435447

Affine planes over finite rings, a summary (DOI)
DOI: 10.1007/S00010-017-0497-4