 if and only if it admits a strictly monotone 0-valuation.  -   $L$ is distributive if and only if it is modular and every strictly monotone 0-valuation on $L$ is a 0-valuation.  -   $L$ is distributive if and only if it admits a strictly monotone 0-valuation.  -   $L$ is distributive if and only if it is modular and every strictly monotone 0-valuation on $L$ is a