Involutive right-residuated l-groupoids

TL;DR

This paper introduces a unifying framework based on integral right-residuated l-groupoids that generalizes various algebraic structures like orthomodular lattices and residuated lattices, connecting them through involutive properties.

Contribution

It proposes a new algebraic framework using integral right-residuated l-groupoids that encompasses multiple known algebraic structures such as MV-algebras and Heyting algebras.

Findings

Unified framework for various algebraic structures

Application to MV-algebras and orthomodular lattices

Generalization of involutive and residuated properties

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.