Closure operations on Intuitionistic Linear algebras
Abstract
In this paper, we introduce the notions of radical filters and extended filters of Intuitionistic Linear algebras (IL-algebras for short) and give some of their properties. The notion of closure operation on an IL-algebra is also introduced as well as the study of some of their main properties. The radical of filters and extended filters are examples of closure operations among several others provided. The class of stable closure operations on an IL-algebra L is used to study the unifying properties of some subclasses of the lattice of filters of L. In particular, we obtain that for a stable closure operation c on an IL-algebra, the collection of c-closed elements of its lattice of filters forms a complete Heyting algebra. Hyperarchimedean IL-algebras are also characterized using closure operations. It is shown that the image of a semi-prime closure operation on an IL-algebra is isomorphic to a quotient IL-algebra. Some properties of the quotients induced by closure operations on an IL-algebra are explored.
Keywords
IL-algebra; closure operation; extended filter; prime filter
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Department of Mathematics, Faculty of Sciences, University of Yaoundé 1 Cameroon
https://orcid.org/0000-0003-3907-1546
Department of Mathematics, Ecole Normale Supérieure de Yaoundé, University of Yaoundé 1 Cameroon
Department of Mathematical Sciences, Saginaw Valley State University United States
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