Hyperaffine planes over hyperrings (Q1923497)

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.