Talk:Field (mathematics)

There is a unique finite field of characteristic <math>p</math> for each power of a prime number <math>p</math>.

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

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)