The Properties of Maximal Filters in Multilattices. (6th July 2022)

• Record Type: Journal Article
• Authors: Awouafack, Daquin Cédric; Fouotsa, Emmanuel
• Other Names: Mynard Frederic Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2022(2022)
• Publication Date: 2022-07-06
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2022/9714656
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : 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.