# Notation related to quotient fields

1. Feb 3, 2013

### fortissimo

1. The problem statement, all variables and given/known data

Let f(x) = x6 + x3 + 1 in Z_2[x]. Show that f(x) is irreducible. Let E = Z_2[x]/(f(x)),
and let α denote the image of x in the quotient field. Show that E* = <α>.

2. Relevant equations

I have solved the first part, but what does E* mean? I have seen the asterix in connection with dual spaces before, but I reckon it means something else here.

3. The attempt at a solution

2. Feb 4, 2013

### fortissimo

It would be nice if someone could give some directions...

3. Feb 4, 2013

### I like Serena

Hi fortissimo!

I do not understand what you mean with the image of x in the quotient field.

But I do know that the star notation in algebra usually means the set without the zero-dividers.
Hope this helps.

4. Feb 4, 2013

Thanks!