Involutive right-residuated l-groupoids

Abstract

A common generalization of orthomodular lattices and residuated lattices is provided corresponding to bounded lattices with an involution and sectionally extensive mappings. It turns out that such a generalization can be based on integral right-residuated l-groupoids. This general framework is applied to MV-algebras,orthomodular lattices, Nelson algebras, basic algebras and Heyting algebras.