When a quotient of a distributive lattice is a boolean algebra

Abstract

In this article, we introduce a lattice congruence with respect to a nonempty ideal $I$ of a distributive lattice $L$ and a derivation $d$ on $L$ denoted by ${\theta }_I^d$. We investigate some necessary and sufficient conditions for the quotient algebra $L/{\theta }_I^d$ to become a Boolean algebra.