## 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.

### MSC:

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

### References:

 [1] Chang C. C.: Algebraic analysis of many valued logics. Trans. Amer. Math. Soc. 88 (1958), 467-490. · Zbl 0084.00704 [2] Chang C. C.: A new proof of the completeness of the Lukasiewicz axioms. Trans. Amer. Math. Soc. 93 (1959), 74-80. · Zbl 0093.01104 [3] Cignoli R. O. L., Mundici D., D’Ottaviano I. M. L.: Algebraic Foundations of Many-valued Reasoning. Kluwer Acad. Publ., Dordrecht-Boston-London, 2000. · Zbl 0937.06009 [4] Rachůnek J.: DRl-semigroups and MV-algebras. Czechoslovak Math. J. 48, 123 (1998), 365-372. · Zbl 0952.06014 [5] Rachůnek J.: MV-algebras are categorically equivalent to a class of DRli-semigroups. Math. Bohemica 123 (1998), 437-441. · Zbl 0934.06014 [6] Rasiova H., Sikorski R.: The Mathematics of Metamathematics. Panstw. Wyd. Nauk., Warszawa, 1963. · Zbl 0122.24311 [7] Turunen E.: Mathematics Behind Fuzzy Logic. Springer Physica-Verlag, Heidelberg-New York, 1999. · Zbl 0940.03029
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