Noetherian and Artinian Lattices
It is proved that if L is a complete modular lattice which is compactly generated, then Rad(L)/0 is Artinian if, and only if for every small element a of L, the sublattice a/0 is Artinian if, and only if L satisfies DCC on small elements.
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/157169 |
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| _version_ | 1841524673838317568 |
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| author | Derya Keskin Tütüncü Sultan Eylem Toksoy Rachid Tribak |
| author_facet | Derya Keskin Tütüncü Sultan Eylem Toksoy Rachid Tribak |
| author_sort | Derya Keskin Tütüncü |
| collection | DOAJ |
| description | It is proved that if L is a complete modular lattice which is compactly generated, then Rad(L)/0 is Artinian if, and only if for every small element a of L, the sublattice a/0 is Artinian if, and only if L satisfies DCC on small elements. |
| format | Article |
| id | doaj-art-f53d6aad68b84f7b963f6f6fc8bc3ca1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f53d6aad68b84f7b963f6f6fc8bc3ca12025-02-03T05:47:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/157169157169Noetherian and Artinian LatticesDerya Keskin Tütüncü0Sultan Eylem Toksoy1Rachid Tribak2Department of Mathematics, Hacettepe University, 06800 Beytepe, Ankara, TurkeyDepartment of Mathematics, İzmir Institute of Technology, 35430 Urla, İzmir, TurkeyCentre Pédagogique Régional (CPR) Tanger, Avenue My Abdelaziz Souani, BP 3117, Tangier 90000, MoroccoIt is proved that if L is a complete modular lattice which is compactly generated, then Rad(L)/0 is Artinian if, and only if for every small element a of L, the sublattice a/0 is Artinian if, and only if L satisfies DCC on small elements.http://dx.doi.org/10.1155/2012/157169 |
| spellingShingle | Derya Keskin Tütüncü Sultan Eylem Toksoy Rachid Tribak Noetherian and Artinian Lattices International Journal of Mathematics and Mathematical Sciences |
| title | Noetherian and Artinian Lattices |
| title_full | Noetherian and Artinian Lattices |
| title_fullStr | Noetherian and Artinian Lattices |
| title_full_unstemmed | Noetherian and Artinian Lattices |
| title_short | Noetherian and Artinian Lattices |
| title_sort | noetherian and artinian lattices |
| url | http://dx.doi.org/10.1155/2012/157169 |
| work_keys_str_mv | AT deryakeskintutuncu noetherianandartinianlattices AT sultaneylemtoksoy noetherianandartinianlattices AT rachidtribak noetherianandartinianlattices |