Hyperaffine planes over hyperrings Original Research Article

The aim of this paper is to construct a geometric structure over both an hyperring and a multiplicative hyperring. In order to accomplish this goal we will need to define a particular class of planar hyperrings. Moreover, the notions of hyperaffine plane, affine map, translation and homothety are given. Finally, in the first case an hyperaffine plane having all homotheties centered in 0 is obtained; in the second case an hyperaffine translation plane is built.