Question

Find quotient ring Z_4[x]/(x*x+1), and define its group of units.

Answer 1

$$I = \left(x ^ {2} + 1\right)$$ $$\mathbb {Z} _ {4} [ x ] / I = \left\{a x + b + I \mid a, b \in \mathbb {Z} _ {4} \right\}$$ $$G = U \left(\mathbb {Z} _ {4} [ x ] / I\right) = \left\{1 + I, 3 + I, 2 x + 1 + I, 2 x + 3 + I, x + I, x + 2 + I, 3 x + I, 3 x + 2 + I \right\}$$