Skew polynomial ring

Summary

A skew polynomial ring $R[x; \sigma]$ is a ring of polynomials over a ring $R$ in which the variable twists the coefficients. The rule is $x a = \sigma(a) x$ for a fixed endomorphism $\sigma$ of $R$. It is the Ore extension with zero derivation. Some authors use the name skew polynomial ring for every Ore extension $R[x; \sigma, \delta]$. Skew polynomial rings over finite fields are used in coding theory, and quantum planes are skew polynomial rings.