Monomial retracts of polynomial rings are polynomial rings

Let $R$ be a ring and $B=R[X_1,\dots ,X_n]$ the polynomial ring in $n$ variables over $R$. In this article, we consider retractions $\phi :B⟶B$ such that $\phi (X_i)$ is either a monic monomial or $0$. We prove that if $R$ is an integral domain, then any such retract is isomorphic to $R^{[p]}$, the polynomial ring in $p$ variables over $R$, for some $0\le p\le n$. We also characterize different monomial retractions of $B$ which give the same retract.