Why is the polynomial $\displaystyle XY$ is irreducible in $\displaystyle R=k[X,XY, XY^2,XY^3,...]$? Assume $\displaystyle XY=pq$ for some $\displaystyle p,q \in R$. I want to show that either $\displaystyle p$ or $\displaystyle q$ are units. Would anyone help me on this?