Free and cyclic hypermodules
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.
scientific article; zbMATH DE number 4061549