Let $K$ be an Algebraic closed field with not necessarily characteristic 0. I'm interested in knowing if $K[x,y,z,\frac{1}{xz}]$ is an integral domain or not.
At first I rewrite my ring as $K[x,y,z,\frac{1}{z},\frac{1}{x}]$, and then I searched over the Internet for some results about Laurent polynomials because it seems like in some way I can use some of their property. I didn't found anything, so I'm asking you some hints or references where to look to solve this problem (if it is possible)
Note that $K[x,y,z,\frac1{xz}]$ is a subring of the quotient field of the integral domain $K[x,y,z]$. Said quotient field is an integral domain itself and hence, any subring of it must be an integral domain.