Hyperaffine planes over hyperrings
type: Item
instance of: scholarly article
title: Hyperaffine planes over hyperrings
zbMATH Open document ID: 0862.51005
DOI: 10.1016/0012-365X(94)00385-V
published in: Discrete Mathematics
publication date: 1996-10-07T00:00:00Z
review text: The author gives the definition of hyperring and multiplicative hyperring. Moreover, the notions of hyperaffine plane, affine map, translation and homothety are given. The author proves that -- associated with a hyperring -- a hyperaffine plane has all homotheties centered in 0, and similarly -- associated with a multiplicative hyperring -- a hyperaffine plane is a translation plane.
Mathematics Subject Classification ID: 51C05
zbMATH DE Number: 932541
zbMATH Keywords: hyperring
zbMATH Keywords: hyperaffine plane
zbMATH Keywords: translation
zbMATH Keywords: homothety
author: R. Rota
reviewed by: Mirosław Uscki
MaRDI profile type: Publication
cites work: Hypergroupes et groupes ordonnes
cites work: Q5604566
cites work: Q3975637
cites work: Q3669592
cites work: Strongly distributive multiplicative hyperrings
cites work: Matroidal hypervector spaces
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description: scientific article; zbMATH DE number 932541