Weierstrass Preparation Theorem - P-adic Analogue

P-adic Analogue

There is an analogous result, also referred to as the Weierstrass preparation theorem, for power series rings over the ring of integers in a p-adic field; namely, a power series f(z) can always be uniquely factored as πn·u(z)·p(z), where u(z) is a unit in the ring of power series, p(z) is a distinguished polynomial (monic, with the coefficients of the non-leading term each in the maximal ideal), and π is a fixed uniformizer.