Some properties of linear right ideal nearrings

Abstract

In a previous paper, we determined all those topological nearrings 𝒩 n whose additive groups are the n -dimensional Euclidean groups, 1$" xmlns:mml="http://www.w3.org/1998/Math/MathML"> n > 1 , and which contain n one-dimensional linear subspaces { J i } i = 1 n which are also right ideals of the nearring with the property that for each w ∈ 𝒩 n , there exist w i ∈ J i , 1 ≤ i ≤ n , such that w = w 1 + w 2 + ⋯ + w n and v w = v w n for each v ∈ 𝒩 n . 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.