On the Lattice of Filters of Intuitionistic Linear Algebras
الموضوعات : Transactions on Fuzzy Sets and Systems
Tenkeu Yannick Lea
1
,
Cyrille Nganteu
2
1 - Department of Mathematics, University of Yaound´e 1, Yaound´e, Cameroon.
2 - Department of Mathematics, University of Yaound´e 1, Yaound´e, Cameroon.
الکلمات المفتاحية: IL-algebra, Filter, Prime filter, Congruence, Residuated lattice.,
ملخص المقالة :
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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