The Properties of Maximal Filters in Multilattices

Daquin Cédric Awouafack, Emmanuel Fouotsa and Frederic Mynard

Journal of Mathematics, 2022, vol. 2022, 1-6

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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9714656

DOI: 10.1155/2022/9714656

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