- #1
BVM
- 9
- 0
In my Abstract Algebra course, it was said that if
[tex] E := \frac{\mathbb{Z}_{3}[X]}{(X^2 + X + 2)}.
[/tex]
The basis of E over [itex]\mathbb{Z}_{3}[/itex] is equal to [itex][1,\bar{X}][/itex].
But this, honestly, doesn't really make sense to me. Why should [itex]\bar{X}[/itex] be in the basis without it containing any other [itex]\bar{X}^n[/itex]? How did they arrive at that exact basis?
[tex] E := \frac{\mathbb{Z}_{3}[X]}{(X^2 + X + 2)}.
[/tex]
The basis of E over [itex]\mathbb{Z}_{3}[/itex] is equal to [itex][1,\bar{X}][/itex].
But this, honestly, doesn't really make sense to me. Why should [itex]\bar{X}[/itex] be in the basis without it containing any other [itex]\bar{X}^n[/itex]? How did they arrive at that exact basis?