Coupled right orthosemirings induced by orthomodular lattices

TL;DR

This paper establishes a novel connection between orthomodular lattices and coupled right orthosemirings, expanding the algebraic framework linking lattice structures and semirings.

Contribution

It introduces coupled right orthosemirings as a new algebraic structure associated with orthomodular lattices, extending previous work on related algebraic systems.

Findings

Defined coupled right orthosemirings for orthomodular lattices

Established correspondence between orthomodular lattices and these semirings

Extended algebraic frameworks for quantum logic structures

Abstract

L. P. Belluce, A. Di Nola and B. Gerla established a connection between MV-algebras and (dually) lattice ordered semirings by means of so-called coupled semirings. A similar connection was found for basic algebras and semilattice ordered right near semirings by the authors. The aim of this paper is to derive an analogous connection for orthomodular lattices and certain semilattice ordered near semirings via so-called coupled right orthosemirings.