# For the greatest... teachers, pupils and "buddys"...Gauss,Riemann,...

Algebra Level 4

Let $$\mathbb{Z} [i] = \{a + bi; a,b \in \mathbb{Z}\text{ and } i =\sqrt{-1}\}$$ to be integers Gaussian set. Which statement(s) below is/are true?

a) $$\mathbb{Z}[i]$$ is an Euclidean Domain.

b) $$\mathbb{Z} [i]$$ is an Principal Ideal Domain.

c) $$\mathbb{Z} [i]$$ is an Unique Factorization Domain

×