On the Lattice of Filters of Intuitionistic Linear Algebras
عنوان مقاله: On the Lattice of Filters of Intuitionistic Linear Algebras
شناسه ملی مقاله: JR_TFSS-2-1_005
منتشر شده در در سال 1402
شناسه ملی مقاله: JR_TFSS-2-1_005
منتشر شده در در سال 1402
مشخصات نویسندگان مقاله:
Tenkeu Yannick Lea - Department of Mathematics, University of Yaounde\۰۳۹;{e} ۱, Yaound\۰۳۹;{e}, Cameroon.
Cyrille Nganteu - Department of Mathematics, University of Yaounde\۰۳۹;{e} ۱, Yaound\۰۳۹;{e}, Cameroon.
خلاصه مقاله:
Tenkeu Yannick Lea - Department of Mathematics, University of Yaounde\۰۳۹;{e} ۱, Yaound\۰۳۹;{e}, Cameroon.
Cyrille Nganteu - Department of Mathematics, University of Yaounde\۰۳۹;{e} ۱, Yaound\۰۳۹;{e}, Cameroon.
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.
کلمات کلیدی: IL-algebra, Filter, Prime filter, Congruence, Residuated lattice.
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1662382/