Properties of non-associative MV-algebras
Ivan Chajda, Helmut Länger · Mathematica Slovaca · 2017
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.