Why we assume henselian ring is local? Henselian ring is defined as local ring in which hensel lemma holds.
Why do we assume local ring?
What is wrong with the definition that 'henselian ring is defined as hensel lemma holds' ?
The version of Hensel's lemma I'm familiar with says that in $\mathbb{Z}_p$, if you have a simple root of a polynomial mod the maximal ideal then it lifts to a simple root. How would you generalize this if there is more than one maximal ideal?
The version of Hensel's lemma I'm familiar with says that in $\mathbb{Z}_p$, if you have a simple root of a polynomial mod the maximal ideal then it lifts to a simple root. How would you generalize this if there is more than one maximal ideal?