International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 65, Pages 4085-4113
doi:10.1155/S0161171203306295
Some properties of linear right ideal nearrings
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.
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.