  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.
