Commutative basic algebras are non-associative generalizations of MV-algebras and form an algebraic semantics of a non-associative generalization of the propositional infinite-valued Łukasiewicz logic. In the paper we investigate additive closure and multiplicative interior operators on commutative basic algebras as a generalization of topological operators.
The authors are very indebted to the anonymous referee for his/her interesting remarks and suggestions.
 Botur, M.—Halaš, R.: Commutative basic algebras and non-associative fuzzy logics, Arch. Math. Logic 48 (2009), 243–255.Search in Google Scholar
 Botur, M.—Halaš, R.—Kühr, J.: States on commutative basic algebras, Fuzzy Sets and Systems 187 (2012), 77–91.Search in Google Scholar
 Botur, M.—Chajda, I.—Halaš, R.: Are basic algebras residuated structures?, Soft Comput 14 (2010), 251–255.Search in Google Scholar
 Chajda, I.—Halaš, R.—Kühr, J.: Many valued quantum algebras, Algebra Universalis 60 (2009), 63–90.Search in Google Scholar
 Chajda, I.—Kühr, J.: Ideals and congruences of basic algebras, Soft Comput 17 (2013), 401–410.Search in Google Scholar
 Galatos, N.—Jipsen, P.—Kowalski, T.—Ono, H.: Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Elsevier, Amsterdam, 2007.Search in Google Scholar
 Jipsen, P.—Tsinakis, C.: A survey of residuated lattices. In: Ordered Algebraic Structures (J. Martinez, ed.), Kluwer, Dordrecht, 2006, pp. 19–56.Search in Google Scholar
 Rachůnek, J.—Šalounová, D.: State operators on commutative basic algebras, WCCI 2012 IEEE World Congress on Computational Intelligence, June 10-15, 2012, Brisbane, Australia, 1511–1516.Search in Google Scholar
 Rachůnek, J.—Švrček, F.: MV-algebras with additive closure operators, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 39 (2000), 183–189.Search in Google Scholar
 Raswiowa, H.—Sikorski, R.: The Mathematics of Metamathematics, Panstw. Wyd. Nauk, Warszawa, 1963.Search in Google Scholar
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