On the Lattice of Filters of Intuitionistic Linear Algebras

Transactions on Fuzzy Sets and Systems

مقاله 6، دوره 2، شماره 1، مرداد 2023، صفحه 72-91   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/tfss.2022.1966200.1046

نویسندگان

Tenkeu J Yannick Lea^* ؛ Cyrille Tchikapa Nganteu

‎Department of Mathematics‎, University of Yaounde\'{e} 1‎, Yaound\'{e}‎, ‎Cameroon‎.

چکیده

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 $(F(\textbf{L}),\subseteq )$ of filters of an IL-algebra $\textbf{L}$ 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.

کلیدواژه‌ها

IL-algebra‎؛ ‎Filter‎؛ ‎Prime filter‎؛ ‎Congruence‎؛ ‎Residuated lattice.‎

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