Notation related to quotient fields

[fortissimo]

Homework Statement

Let f(x) = x6 + x3 + 1 in Z_2[x]. Show that f(x) is irreducible. Let E = Z_2[x]/(f(x)),
and let αdenote the image of x in the quotient field. Show that E* = <α>.

Homework 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.

The Attempt at a Solution

 

[fortissimo]

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

 

[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.

 

[fortissimo]

Thanks!