\indent let $k$ be of a field of characteristic $0$. the first weyl algebra $a_1(k) = k/(yx-xy-1)$ is $z$-graded with deg$(x) = 1$, deg$(y) = -1$, and is a simple ring of $gk$-dimension $2$. sierra has studied its category of graded modules and shown how to find all $z$-graded algebras with an equivalent graded module category. smith has also shown how the geometry of this example is related to a certain stack. our goal is to study more general classes of $z$-graded simple rings to find more examples which may have interesting algebraic and geometric properties. specifically, we study the structure of $z$-graded simple rings $a$ with graded quotient ring $q$ such that $q_0$ is a field with trdeg $q_0 = gk a - 1$. as a special case, we can classify all $z$-graded simple rings of $gk$-dimension $2$. this is joint work with jason bell.