Originally Posted by
knguyen2005 Find all the maximal ideals of :
(i) Real number IR
$\displaystyle \mathbb{R}$ is a field. thus ...
(ii) Integers Z
$\displaystyle \mathbb{Z}$ is a PID. the maximal ideals are in the form $\displaystyle p\mathbb{Z},$ where $\displaystyle p$ is any prime.
(iii) C[x]
$\displaystyle \mathbb{C}[x]$ is a PID. the maximal ideals are in the form $\displaystyle <x-a>,$ where $\displaystyle a \in \mathbb{C}.$ that is because $\displaystyle \mathbb{C}$ is algebraically closed.
(iv) Z_60
let $\displaystyle \{p_1, \cdots , p_k \}$ be the set of prime divisors of $\displaystyle n> 1.$ then $\displaystyle \mathbb{Z}/n\mathbb{Z}$ has exactly $\displaystyle k$ maximal ideals: $\displaystyle m_j = p_j \mathbb{Z}/n \mathbb{Z}, \ 1 \leq j \leq k.$ (also see (ii))
I got no idea how to do it, so I couldn't attempt these questions. Sorry
Can some body show me how to do it please?
Thank you very much