A class of multiplicative lattices

TL;DR

This paper investigates a specific class of multiplicative lattices characterized by a unique algebraic identity involving elements and their residuals, expanding understanding of their structure.

Contribution

It introduces and analyzes a new class of multiplicative lattices defined by a particular algebraic condition involving residuals.

Findings

Characterization of the algebraic structure of these lattices

Identification of properties that distinguish this class

Potential applications in lattice theory and algebra

Abstract

We study the multiplicative lattices L which satisfy the condition a = (a : (a : b))(a : b) for all a,b in L.