International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 11, Pages 663-674

Linear right ideal nearrings

Kenneth D. Magill Jr.

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.


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 w𝒩n, we require that there exist wiJi, 1in, 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 v𝒩n.