International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 11, Pages 663-674
doi:10.1155/S0161171201006810
Linear right ideal nearrings
Mathematics Building, Rm. 244, SUNY at Buffalo, Buffalo 14260-2900, NY, USA
Received 16 February 2001
Copyright © 2001 Kenneth D. Magill. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We determine, up to isomorphism, 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 satisfying several additional properties. Specifically, for each w∈𝒩n, we require that there exist wi∈Ji, 1≤i≤n, such that w=w1+w2+⋯+wn and multiplication on the left of w yields the same result as multiplication by the same element on the left of wn. That is, vw=vwn for each v∈𝒩n.