Linear right ideal nearrings

Kenneth D. Magill

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 27, 1-12

Abstract:

We determine, up to isomorphism, all those topological nearrings 𝒩 n whose additive groups are the n -dimensional Euclidean groups, n > 1 , and which contain n one-dimensional linear subspaces { J i } i = 1 n which are also right ideals of the nearring satisfying several additional properties. Specifically, for each w ∈ 𝒩 n , we require that there exist w i ∈ J i , 1 ≤ i ≤ n , such that w = w 1 + w 2 + ⋯ + w n and multiplication on the left of w yields the same result as multiplication by the same element on the left of w n . That is, v w = v w n for each v ∈ 𝒩 n .

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:126581

DOI: 10.1155/S0161171201006810

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