Distinguished polynomial
= Distinguished polynomial
{title2=$f(T)=T^d+a_{d-1}T^{d-1}+\cdots+a_0,\quad a_i\in p\mathbb Z_p$}
A distinguished polynomial over $\mathbb Z_p$ is monic and has every non-leading coefficient divisible by $p$. The <Weierstrass preparation theorem> expresses any nonzero element of $\mathbb Z_p[[T]]$ as a power of $p$ times a unit times a distinguished polynomial.