On the Lattice of Filters of Intuitionistic Linear Algebras

Subject Areas : Transactions on Fuzzy Sets and Systems

Tenkeu Yannick Lea ¹ (Department of Mathematics, University of Yaound´e 1, Yaound´e, Cameroon.)
Cyrille Nganteu ² (Department of Mathematics, University of Yaound´e 1, Yaound´e, Cameroon.)

Received: 2022-08-24 Accepted : 2022-12-30 Published : 2023-05-01

Keywords: IL-algebra‎, ‎Filter‎, ‎Prime filter‎, ‎Congruence‎, ‎Residuated lattice.‎,

Abstract :

In this paper, we investigate the filter theory of Intuitionistic Linear Algebra (IL-algebra, in short) with emphasis on the lattice of filters of IL-algebras and relationship between filters and congruences on IL-algebras. We characterize the filter generated by a subset and give some related properties. The prime filter for IL-algebras is characterized and the prime filter theorem for IL-algebra is established. We get that the lattice (F (L), ⊆) of filters of an IL-algebra L is algebraic, Brouwerian, pseudocomplemented and endowed with the structure of Heyting algebra. We prove that the lattice of congruences and that of filters of any IL-algebra are isomorphic.

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