Henselian rings and Weierstrass polynomials

Abstract:

We give two characterizations of a one-dimensional Henselian domain. If $\left ( {A,\mathcal {M}} \right )$ is a local domain of Krull dimension at least two, or if $\left ( {A,\mathcal {M}} \right )$ is a one-dimensional Henselian local domain, then a polynomial $f$ in $A\left [ T \right ]$ is Weierstrass if and only if $\left ( {\mathcal {M},T} \right )$ is the only maximal ideal of $A\left [ T \right ]$ that contains $f$.