= Skew Laurent polynomial ring
{title2=$A[t,t^{-1};\sigma]$}
Adjoining an inverse of $t$ to the <skew polynomial ring of an automorphism> allows finite sums $\sum_{j\in\mathbb Z}a_jt^j$, with $ta=\sigma(a)t$. Every element can be moved into the polynomial subring by multiplying by a sufficiently large power of $t$. Consequently, for a <right ideal> $I$ of this <ring>, $I$ is generated by its intersection with the polynomial subring: if $ft^N$ lies there, then $f=(ft^N)t^{-N}$. This proves transfer of right <Noetherianity> from the polynomial subring, and multiplication on the left proves the left-handed version.
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