Free and cyclic hypermodules
type: Item
instance of: scholarly article
title: Free and cyclic hypermodules
zbMATH Open document ID: 0651.20077
DOI: 10.1007/BF01761468
author: Ch. G. Massouros
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1988-01-01T00:00:00Z
review text: The notion of hypermodule is studied. Let P be a unitary hyperring. A left hypermodule over P is a canonical hypergroup \((M,+)\) with an external multiplication \(\mu\) : \(P\times M\to M\), \(\mu (a,m)=am\), satisfying the conditions: i) \(a(m+n)=am+an\); ii) \((a+b)m=am+bm\); iii) \((ab)m=a(bm)\); iv) \(1m=m\) for all \(a,b\in P\), \(m,n\in M\). The author gives an example having nice applications in finite geometries, analytic projective geometries and the euclidean spherical geometries. The concepts of free hypermodule and cyclic hypermodule are also introduced and studied in the paper.
Mathematics Subject Classification ID: 20N99
zbMATH DE Number: 4061549
zbMATH Keywords: hyperring
zbMATH Keywords: left hypermodule
zbMATH Keywords: canonical hypergroup
zbMATH Keywords: finite geometries
zbMATH Keywords: projective geometries
zbMATH Keywords: free hypermodule
zbMATH Keywords: cyclic hypermodule
reviewed by: Mirela Ştefănescu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4061549