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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

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