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  "body": "\n## Summary\n\nA skew polynomial ring $R[x; \\sigma]$ is a ring of polynomials over a [[ring|0B1261B5ED]] $R$ in which the variable twists the coefficients.\nThe rule is $x a = \\sigma(a) x$ for a fixed endomorphism $\\sigma$ of $R$.\nIt is the [[Ore extension|VF3PV13BA1]] with zero derivation.\nSome authors use the name skew polynomial ring for every Ore extension $R[x; \\sigma, \\delta]$.\nSkew polynomial rings over finite fields are used in coding theory, and quantum planes are skew polynomial rings.\n\n## Explanations\n\n### L1 human\n\nPolynomials are added as usual, but multiplying $x$ past a coefficient $a$ replaces it with $\\sigma(a)$.\nOver the complex numbers with $\\sigma$ the complex conjugation, $x \\cdot i = -i \\cdot x$.\nSo $x$ anticommutes with $i$ but commutes with real numbers.\nThe order of factors now matters, while every element is still a sum $a_0 + a_1 x + \\cdots + a_n x^n$.\n",
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