Affiliation:
1. Department of Algebra and Geometry Palacký University Olomouc 17. listopadu 12 CZ–771 46 Olomouc Czech Republic
2. Institute of Discrete Mathematics and Geometry TU Wien Wiedner Hauptstraße 8-10 A–1040 Vienna Austria
Abstract
Abstract
Non-associative MV-algebras (NMV-algebras) (A, ⊕, ¬, 0) were introduced in [CHAJDA, I.—KÜHR, J.: A non-associative generalization of MV-algebras, Math. Slovaca 57 (2007), 301–312]. In the present paper we prove some properties of these algebras, investigate when intervals of the form [a, 1] can be made into NMV-algebras in some natural way and consider idempotent elements and derivations of NMV-algebras. Moreover, we study decompositions of NMV-algebras and characterize the congruences on NMV-algebras by means of so-called filters.
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