Which of the following is/are prime as well as maximal ideals of \(\mathbb{Z}_{28}\)-
(a) \(2\mathbb{Z}\)
(b) \(4\mathbb{Z}\)
(c) \(7\mathbb{Z}\)
(d) \(14\mathbb{Z}\)
Explanation: (a) and (c) are the correct answers.
Note: In \(\mathbb{Z}_m, n\mathbb{Z}\) is prime and maximal iff \(n\mid m\) and \(n\) is prime.
Tags:
Rings