Talk:Field (mathematics)

There is a unique finite field of characteristic $p$ for each power of a prime number $p$.

I don't think that this common truth requires a {{prove}} tag: An field of $p^{n}$ elements can easily be constructed as an extension of a field with $p$ elements, e.g., $\mathbb {Z} _{p}$: just look at the zeroes of $x^{p^{n}}-x\in \mathbb {Z} _{p}[x]$ in the algebraic closure ${\overline {\mathbb {Z} }}_{p}$ .

This field is unique (up to isomorphism, of course), as the multiplicative group of a finite field is cyclic.

--BRichtigen 12:06, 5 November 2008 (EST)