A note on distributivity of the lattice of $L$-ideals of a ring

Abstract

Many studies have investigated the lattice of fuzzy substructures of algebraic structures such as groups and rings. In this study, we prove that the lattice of $L$-ideals of a ring is distributive if and only if the lattice of its ideals is distributive, for an infinitely $\vee$-distributive lattice $L$.