  We study consequences of a monoidal categorification of the unipotent quantum
coordinate ring $A_q(\mathfrak{n}(w))$ together with the Laurent phenomenon of
cluster algebras. We show that if a simple module $S$ in the category $\mathcal
C_w$ strongly commutes with all the cluster variables in a cluster $[ \mathscr
C]$, then $[S]$ is a cluster monomial in $[ \mathscr C ]$. If $S$ strongly
commutes with cluster variables except exactly one cluster variable $[M_k]$,
then $[S]$ is either a cluster monomial in $[\mathscr C ]$ or a cluster
monomial in $\mu_k([ \mathscr C ])$. We give a new proof of the fact that the
upper global basis is a common triangular basis (in the sense of Fan Qin) of
the localization $\widetilde A_q(\mathfrak{n}(w))$ of $A_q(\mathfrak{n}(w))$ at
the frozen variables. A characterization on the commutativity of a simple
module $S$ with cluster variables in a cluster $[ \mathscr C]$ is given in
terms of the denominator vector of $[S]$ with respect to the cluster $[
\mathscr C]$.
