MV-algebras with additive closure operators. (English) Zbl 1039.06005

Summary: In the paper, closure MV-algebras (i.e. MV-algebras with additive closure operators) are introduced and studied as generalizations of topological Boolean algebras. In particular, closure MV-algebras determined by idempotent elements, connections between closure MV-algebras and induced topological Boolean algebras and closed ideals in connection with congruences of MV-algebras are examined.


06D35 MV-algebras
06A15 Galois correspondences, closure operators (in relation to ordered sets)
06E05 Structure theory of Boolean algebras


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