= Skew Laurent extensions of domains are domains
{title2=$\operatorname{lc}(fg)=a_m\sigma^m(b_n)$}
Let $A$ have no zero divisors and $\sigma$ be an <automorphism>. For nonzero <Laurent polynomials> $f=\sum a_ix^i$ and $g=\sum b_jx^j$ with greatest exponents $m,n$, the coefficient of $x^{m+n}$ in $fg$ is $a_m\sigma^m(b_n)$. No other exponent pair contributes to that highest degree. Both factors are nonzero, so their product is nonzero, proving the <noncommutative domain> property in every characteristic.
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