Wenfong Ke, Hubert Kiechle, Günter Pilz, Gerhard Wendt,
, in American Mathematical Society: Contemporary Mathematics, in Contemporary Mathematics, Vol. 658, American Mathematical Society, Providence, RI, USA, Seite(n) 187-196, 2016, ISBN: 978-1-4704-2902-7
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A map f from a vector space V into its underlying field F is called semi-homogeneous if f(kv)=kf(v) holds for all k in Im(f) and v in V. This means that we have f(f(w)v)=f(w)f(v) for all v,w in V. If we define the operation * on V via w*v:=f(w)v, this equation makes (V,+,*) into a planar nearring. So we have an (almost) 1-1-correspondence between semi-homogeneous maps and planar nearrings on a vector space V. This enables a complete characterization of semi-homogeneous maps. One can even generalize this to the much more general case of actions of groups on sets.