Cofinitely (Weak) G-Supplemented Lattices
In this work, cofinitely (weak) g-supplemented lattices are defined and some properties of these lattices are investigated. It is shown that quotient sublattices of cofinitely (weak) g-supplemented lattices are cofinitely (weak) g-supplemented. If 〖{a_i/0} 〗_(i∈I) is a collection of cofinitely (weak...
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| Format: | Article |
| Language: | English |
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Düzce University
2022-01-01
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| Series: | Düzce Üniversitesi Bilim ve Teknoloji Dergisi |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/1982731 |
| _version_ | 1797300867246850048 |
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| author | Sultan Eylem Toksoy |
| author_facet | Sultan Eylem Toksoy |
| author_sort | Sultan Eylem Toksoy |
| collection | DOAJ |
| description | In this work, cofinitely (weak) g-supplemented lattices are defined and some properties of these lattices are investigated. It is shown that quotient sublattices of cofinitely (weak) g-supplemented lattices are cofinitely (weak) g-supplemented. If 〖{a_i/0} 〗_(i∈I) is a collection of cofinitely (weak) g-supplemented sublattices of L and 1=⋁_(i∈I) a_i, then L is also cofinitely (weak) g-supplemented. It is proved that without loss of generality weak g-supplements of cofinite elements in compactly generated lattices are compact. An example showing that this is not true for lattices which are not cofinitely generated is given. A condition is given under which a compactly generated cofinitely weak g-supplemented lattice is cofinitely g-supplemented. |
| first_indexed | 2024-03-07T23:13:07Z |
| format | Article |
| id | doaj.art-9c26c8dcc7a345e7ae44e03e9a29703f |
| institution | Directory Open Access Journal |
| issn | 2148-2446 |
| language | English |
| last_indexed | 2024-03-07T23:13:07Z |
| publishDate | 2022-01-01 |
| publisher | Düzce University |
| record_format | Article |
| series | Düzce Üniversitesi Bilim ve Teknoloji Dergisi |
| spelling | doaj.art-9c26c8dcc7a345e7ae44e03e9a29703f2024-02-21T14:07:30ZengDüzce UniversityDüzce Üniversitesi Bilim ve Teknoloji Dergisi2148-24462022-01-0110147648210.29130/dubited.99751897Cofinitely (Weak) G-Supplemented LatticesSultan Eylem Toksoy0HACETTEPE UNIVERSITY, FACULTY OF SCIENCE, DEPARTMENT OF MATHEMATICSIn this work, cofinitely (weak) g-supplemented lattices are defined and some properties of these lattices are investigated. It is shown that quotient sublattices of cofinitely (weak) g-supplemented lattices are cofinitely (weak) g-supplemented. If 〖{a_i/0} 〗_(i∈I) is a collection of cofinitely (weak) g-supplemented sublattices of L and 1=⋁_(i∈I) a_i, then L is also cofinitely (weak) g-supplemented. It is proved that without loss of generality weak g-supplements of cofinite elements in compactly generated lattices are compact. An example showing that this is not true for lattices which are not cofinitely generated is given. A condition is given under which a compactly generated cofinitely weak g-supplemented lattice is cofinitely g-supplemented.https://dergipark.org.tr/tr/download/article-file/1982731modüler kafesg-küçük elemanlarg-tümlenmiş kafeslermodular latticesg-small elementsg-supplemented lattices |
| spellingShingle | Sultan Eylem Toksoy Cofinitely (Weak) G-Supplemented Lattices Düzce Üniversitesi Bilim ve Teknoloji Dergisi modüler kafes g-küçük elemanlar g-tümlenmiş kafesler modular lattices g-small elements g-supplemented lattices |
| title | Cofinitely (Weak) G-Supplemented Lattices |
| title_full | Cofinitely (Weak) G-Supplemented Lattices |
| title_fullStr | Cofinitely (Weak) G-Supplemented Lattices |
| title_full_unstemmed | Cofinitely (Weak) G-Supplemented Lattices |
| title_short | Cofinitely (Weak) G-Supplemented Lattices |
| title_sort | cofinitely weak g supplemented lattices |
| topic | modüler kafes g-küçük elemanlar g-tümlenmiş kafesler modular lattices g-small elements g-supplemented lattices |
| url | https://dergipark.org.tr/tr/download/article-file/1982731 |
| work_keys_str_mv | AT sultaneylemtoksoy cofinitelyweakgsupplementedlattices |