Let $F$ a field and let $D$ an element of an extension $K/F$ such that $D$ is not the square of any element of $F$. Does there exists an irreducible polynomial in $F[X]$ with discriminant $D$? Are there sufficient conditions for such polynomial to exists e.g. $char F\neq 2$?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
Here's how it works:
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top