 Skew polynomial ring of an automorphism

For an automorphism $\sigma$ of a unital ring $A$, this ring consists of finite sums ${\sum }_{j\ge 0}{a}_j{t}^j$, with multiplication determined by $ta=\sigma (a)t$. Both left and right coefficient normal forms are available because $\sigma$ is invertible. The noncommutative Hilbert basis theorem implies that it is a right Noetherian ring when $A$ is, and a left Noetherian ring when $A$ is. Invertibility of $\sigma$ matters in this two-sided formulation.