Some properties of linear right ideal nearrings

Abstract

In a previous paper, we determined all those topological nearrings 𝒩n whose additive groups are the n-dimensional Euclidean groups, n>1, and which contain n one-dimensional linear subspaces {Ji}i=1n which are also right ideals of the nearring with the property that for each w∈𝒩n, there exist wi∈Ji, 1≤i≤n, such that w=w1+w2+⋯+wnand vw=vwn for each v∈𝒩n. In this paper, we determine the properties of these nearrings, their ideals, and when two of these nearrings are isomorphic, and we investigate the multiplicative semigroups of these nearrings.