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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Published in | IAENG international journal of applied mathematics Vol. 50; no. 3; pp. 1 - 5 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Hong Kong
International Association of Engineers
01.09.2020
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 1992-9978 1992-9986 |