  We investigate Krull dimensions of semirings and semifields dealt in tropical
geometry. We prove that for a congruence $C$ on a tropical Laurent polynomial
semiring $\boldsymbol{T}[X_1^{\pm}, \ldots, X_n^{\pm}]$ including a finite
subset whose congruence variety is equal to the congruence variety
$\boldsymbol{V}(C)$ associated with $C$, the Krull dimension of the quotient
semiring $\boldsymbol{T}[X_1^{\pm}, \ldots, X_n^{\pm}] / C$ coincides with the
dimension of $\boldsymbol{V}(C)$ as a polyhedral complex plus one when
$\boldsymbol{V}(C)$ is nonempty. With this fact, we also show that rational
function semifields of tropical curves which do not consist of only one point
have Krull dimension two.
