cmi-entrance 2020 Q10

cmi-entrance · India · pgmath 4 marks Groups Ring and Field Structure

Let $f(x) = x^{2} + ax + b \in \mathbb{F}_{3}[X]$. What is the number of non-isomorphic quotient rings $\mathbb{F}_{3}[X] / (f(X))$?

Let $f(x) = x^{2} + ax + b \in \mathbb{F}_{3}[X]$. What is the number of non-isomorphic quotient rings $\mathbb{F}_{3}[X] / (f(X))$?