Exercise
Consider f =
Xn + 1 
Q[X].
For which positive integers n is Q[X]/(f) a monoid?
None
All
n > 1
Wrong.
Right.
No, the unit also exists for residue class rings if n = 1.
Exercise
Consider f =
Xn + 1 Q[X].
For which positive integers n is Q[X]/(f) a monoid?
None
All
n > 1