  Let $R$ be an integral domain and $B=R[x_1,\ldots,x_n]$ be the polynomial
ring. In this paper, we consider retracts of $B[1/M]$ for a monomial $M$. We
show that (1) if $M=\prod_{i=1}^nx_i$, then every retract is a Laurent
polynomial ring over $R$, (2) if $R$ is a perfect field and $n=3$, then every
retract is isomorphic to $R[y_1^{\pm1},\ldots,y_s^{\pm1},z_1,\ldots,z_t]$ for
some $s,t\geq 0$.

Commutative Algebra;Algebraic Geometry