Word Count : 338

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Let's determine if the set \( (3) \) is a maximal ideal in \( \mathbb{Z}_9 \). ### Step 1: Understand the ideal \( (3) \) The ideal \( (3) \) in \( \mathbb{Z}_9 \) consists of all multiples of 3 in \( \mathbb{Z}_9 \). These elements are: \[ (3) = \{ 0, 3, 6 \} \] _________ _____ _____ _____ __________ ________.
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