Linear right ideal nearrings
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,...
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Hindawi Limited
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201006810 |
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doaj-af19a03ff4854755a50c0c65fb0d9fbd2020-11-24T21:28:20ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01271166367410.1155/S0161171201006810Linear right ideal nearringsKenneth D. Magill0Mathematics Building, Rm. 244, SUNY at Buffalo, Buffalo 14260-2900, NY, USAWe 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.http://dx.doi.org/10.1155/S0161171201006810 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Kenneth D. Magill |
| spellingShingle |
Kenneth D. Magill Linear right ideal nearrings International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Kenneth D. Magill |
| author_sort |
Kenneth D. Magill |
| title |
Linear right ideal nearrings |
| title_short |
Linear right ideal nearrings |
| title_full |
Linear right ideal nearrings |
| title_fullStr |
Linear right ideal nearrings |
| title_full_unstemmed |
Linear right ideal nearrings |
| title_sort |
linear right ideal nearrings |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2001-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/S0161171201006810 |
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AT kennethdmagill linearrightidealnearrings |
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