On Dummit's paper

Question

I have been recently reading Dummit's paper on solvability of quintic polynomials. At certain point, he mentiones that all results are valid "over any field $K$ of characteristic different from 2 and 5."

I would like to know if the real field satisfies that. Also what does it mean in order words?

Also, any elementary references on Abstract Algebra would be appreciated.

Thanks

Answer 1

One way of thinking about the characteristic of a field is it's the smallest number of times you add $1$ to itself to get back to $0$. For example, in $\mathbb{Z}/2\mathbb{Z}$, $1 + 1 = 0$, so the characteristic is $2$. For fields like $\mathbb{R}$ and $\mathbb{Q}$ where you will never get to $0$ by adding strings of $1$, we say the characteristic is $0$.