Automorphisms of Z_3

1. Apr 22, 2007

erraticimpulse

Please bear with me as I don't have latex. This is a homework question I have and I don't even know if it makes sense:

How many Z_3 (set of integers modulo 3) vector space automorphisms of Z_3(alpha) are there? Describe them.

I'm not sure if alpha is supposed to be the root of some polynomial or just an element outside of Z_3. I know that Z_3 is isomorphic to GF(3) (the Galois field of order 3). Any help would be much appreciated.

2. Apr 22, 2007

matt grime

If you don't know what alpha is, then we have no chance of knowing what it is. The only person who can help you here is you: find out from your book, notes, the question sheet, what alpha is.

3. Apr 22, 2007

erraticimpulse

Okay well, I figured it out. Alpha was defined a few pages earlier as a root of x^2+1 (a polynomial with coeff's in Z_3[x]). Thanks for pointing out what should have been obvious to me.

4. Apr 22, 2007

matt grime

So Z_3[alpha] is just a 2 dimensional vector space over Z_3, so we're just looking at the invertible 2x2 matrices over Z_3. What answer did you get?