The Lattices of Monadic Filters in Monadic BL-algebras

In this paper, we focus on lattice structures of the set of monadic filters (monadic filters, stable monadic filters, involutory monadic filters) of monadic BL-algebras and prove that (a) the classes of all monadic filters in monadic BL-algebras forms a complete Heyting algebras with respect to incl...

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Bibliographic Details
Published inIAENG international journal of applied mathematics Vol. 50; no. 3; pp. 1 - 5
Main Authors Wang, Juntao, Wang, Mei
Format Journal Article
LanguageEnglish
Published Hong Kong International Association of Engineers 01.09.2020
Subjects
Boolean
Boolean algebra
Lattices (mathematics)
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Summary:In this paper, we focus on lattice structures of the set of monadic filters (monadic filters, stable monadic filters, involutory monadic filters) of monadic BL-algebras and prove that (a) the classes of all monadic filters in monadic BL-algebras forms a complete Heyting algebras with respect to inclusion; (b) the class of all stable monadic filters relative a monadic filter F in monadic BL-algebras is a complete Boolean algebra with respect to inclusion; (c) the class of all involutory monadic filters relative a monadic filter F in monadic BL-algebras is a complete Boolean algebra with respect to inclusion. These results also provide the solid foundation to study the variety of monadic BL-algebras.
ISSN:1992-9978
1992-9986