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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| Format: | Article |
| Language: | English |
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Wiley
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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| _version_ | 1832554306541191168 |
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| author | Kenneth D. Magill |
| author_facet | Kenneth D. Magill |
| author_sort | Kenneth D. Magill |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-af19a03ff4854755a50c0c65fb0d9fbd |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-af19a03ff4854755a50c0c65fb0d9fbd2025-02-03T05:51:58ZengWileyInternational 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 |
| spellingShingle | Kenneth D. Magill Linear right ideal nearrings International Journal of Mathematics and Mathematical Sciences |
| title | Linear right ideal nearrings |
| title_full | Linear right ideal nearrings |
| title_fullStr | Linear right ideal nearrings |
| title_full_unstemmed | Linear right ideal nearrings |
| title_short | Linear right ideal nearrings |
| title_sort | linear right ideal nearrings |
| url | http://dx.doi.org/10.1155/S0161171201006810 |
| work_keys_str_mv | AT kennethdmagill linearrightidealnearrings |