Does anyone know anything about the normal regular sequences in the quantum plane?

Here are the definitions:

Normal regular sequence: Let $R$ be a ring (not necessarily commutative). A sequence $x_1, \ldots, x_n$ is a normal regular sequence in $R$ if

1) $x_1$ is a normal, regular element in $R$, and

2) $x_i$ is normal, regular element in $R/(x_1, \ldots, x_{i-1})$ for all $2 \leq i \leq n$.

Quantum plane: A $k$-algebra generated by $x, y$ subject to the relation $yx = qxy$, denoted by $k_q[x, y]$, that is, $$k_q[x, y] = \frac{k\langle x, y\rangle}{(yx - qxy)}. $$ Here $q\in k$ is a primitive root of 1.

The length of any regular sequence in $k_q[x, y]$ is no more than 2, and I know there is some result about such normal regular sequence when $x_1, x_2$ are homogeneous elements. But anything else?

Thanks,