The Properties of Maximal Filters in Multilattices
Daquin Cèdric Awouafack, Emmanuel Fouotsa · Journal of Mathematics · 2022
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.