Let $I = \{a+ ib \in \Bbb Z[i] : 2 \mid a-b\}$ then $I$ is a maximal ideal of $ \Bbb Z[i]$.
69352
Prove that $I= \{a+bi \in ℤ[i] : a≡b \pmod{2}\}$ is an maximal ideal of $ℤ[i]$.
157876
If every prime ideal is maximal, what can we say about the ring?
18186
Prove that ideal $I = \langle X^2,X+1\rangle$ is principal or not (in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$ )
136710
Prove that for every $a\in A$ $\exists$ $q\in M,s\in A$ s.t. $a=sba+qa$ where $M$ is maximal ideal in $A$.
68202
Must an ideal generated by an irreducible element be a maximal ideal?
22716
$A$ is integrally closed if and only if $A_P$ is integrally closed for all maximal ideals $P$ of $A$.
90314
Maximal ideals in $R[x]$
45684
Is quotient of a ring by a power of a maximal ideal local?
110022
Showing prime and maximal ideal
63207
Zorn's lemma and maximal ideals
42170
$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element
17239
Find all ideals of ${\mathbb{Z}_n}$
30714
A question on ring homomorphisms and maximal ideals.
84663
$A$ local Noetherian ring with principal maximal ideal implies PIR?
104782
Polynomial irreducible - maximal ideal
129371
Maximal ideals in the ring of real functions on $[0,1]$
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$