International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 65, Pages 4085-4113

Some properties of linear right ideal nearrings

K. D. Magill Jr.

Department of Mathematics, State University of New York at Buffalo, Buffalo 14260-2900, NY, USA

Received 9 June 2003

Copyright © 2003 K. 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.


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 w𝒩n, there exist wiJi, 1in, such that w=w1+w2++wnand vw=vwn for each v𝒩n. 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.