Weak MV-algebras

In a recent paper [CHAJDA, I.-KUHR, J.: A non-associative generalization of MV-algebras, Math. Slovaca 57, (2007), 301-312], authors introduced and studied a non-associative generalization of MV-algebras called NMV-algebras. In contrast to MV-algebras, sections (i.e. principal filters) in NMV-algebras which are proper (i.e. are not MV-algebras), do not admit a structure of an NMV-algebra with respect to the operations defined in a natural way. The aim of the paper is to present a new class of algebras generalizing MV-algebras but sharing the above property.