= Unit of a Laurent polynomial ring
{title2=$(R[t,t^{-1}])^\times=\{ut^k:u\in R^\times,\ k\in\mathbb Z\}$}
= Laurent unit
{c}
{synonym}
For an <integral domain> $R$, the <breadth of a Laurent polynomial> adds under multiplication. If two Laurent <polynomials> multiply to one, both therefore have breadth zero: they are <monomials>, and their coefficients must be <units> of $R$. Conversely every displayed monomial is invertible. For $R=\mathbb Z$ the units are precisely $\pm t^k$, explaining the normalization ambiguity of an <Alexander polynomial>.
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