On non-associative generalizations of MV-algebras and lattice-ordered commutative loops

The aim of the paper is to describe the connections between lattice-ordered commutative loops and certain “basic algebras” which are a non-associative generalization of MV-algebras and are related to commutative semicopulas. This extends the well-known equivalence between lattice-ordered Abelian groups with strong order-unit and MV-algebras.