The Properties of Maximal Filters in Multilattices
Jacobson’s radical of a filter F is the intersection of all maximal filters containing F. We present several properties of maximal filters in multilattices. As a consequence of Zorn’s lemma, we prove that each proper filter is contained in a maximal filter. When the filter lattice is distributive, w...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9714656 |
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| author | Daquin Cédric Awouafack Emmanuel Fouotsa |
| author_facet | Daquin Cédric Awouafack Emmanuel Fouotsa |
| author_sort | Daquin Cédric Awouafack |
| collection | DOAJ |
| description | Jacobson’s radical of a filter F is the intersection of all maximal filters containing F. We present several properties of maximal filters in multilattices. As a consequence of Zorn’s lemma, we prove that each proper filter is contained in a maximal filter. When the filter lattice is distributive, we prove that each maximal filter is prime. Finally, we determine Jacobson’s radical of filters in multilattices. |
| format | Article |
| id | doaj-art-ceae3c7fb2f94238872112b0e91c65c9 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ceae3c7fb2f94238872112b0e91c65c92025-02-03T06:12:25ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/9714656The Properties of Maximal Filters in MultilatticesDaquin Cédric Awouafack0Emmanuel Fouotsa1Mathematics and Computer Science DepartmentMathematics and Computer Science DepartmentJacobson’s radical of a filter F is the intersection of all maximal filters containing F. We present several properties of maximal filters in multilattices. As a consequence of Zorn’s lemma, we prove that each proper filter is contained in a maximal filter. When the filter lattice is distributive, we prove that each maximal filter is prime. Finally, we determine Jacobson’s radical of filters in multilattices.http://dx.doi.org/10.1155/2022/9714656 |
| spellingShingle | Daquin Cédric Awouafack Emmanuel Fouotsa The Properties of Maximal Filters in Multilattices Journal of Mathematics |
| title | The Properties of Maximal Filters in Multilattices |
| title_full | The Properties of Maximal Filters in Multilattices |
| title_fullStr | The Properties of Maximal Filters in Multilattices |
| title_full_unstemmed | The Properties of Maximal Filters in Multilattices |
| title_short | The Properties of Maximal Filters in Multilattices |
| title_sort | properties of maximal filters in multilattices |
| url | http://dx.doi.org/10.1155/2022/9714656 |
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