On l-implicative-groups and associated algebras of logic

Abstract

The l-implicative-group is a term equivalent definition of the group coming from algebras of logic. In this paper, we study the representability of l-implicative-groups and of associated algebras of logic. First, we find equivalent conditions for an l-implicative-group to be representable. Then, we prove that representability at the l-implicative-group level is inherited by the algebras obtained by restricting the l-implicative-group operations to the negative, positive cones.