Why isn't $\{0\}$ being prime ideal is not maximal in $\mathbb{Z}$?
53367
In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?
81982
Is $\mathbb{Z}[x]$ a principal ideal domain?
52602
$K[X^2,X^3]\subset K[X]$ is a Noetherian domain and all its prime ideals are maximal
37929
Classification of prime ideals of $\mathbb{Z}[X]$
107454
Why D/I is finite if I is a non-zero ideal of the ring of integers of a number field?
63207
Zorn's lemma and maximal ideals
53469
C(0, 1) has infinitely many prime ideals not of the form Mp
28244
Is the ideal $I = \{f\mid f (0) = 0\}$ in the ring $C [0, 1]$ of all continuous real valued functions on $[0, 1]$ a maximal ideal?
133975
Localising a polynomial ring and non-maximal prime ideal
31585
Primary ideals of $\mathbb{Z}$
29126
Maximal ideal in the ring of continuous functions from $\mathbb{R} \to \mathbb{R}$
87780
Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
54916
Maximal ideal in commutative ring
21946
What do prime ideals in $k[x,y]$ look like?
93658
Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible
113582
How can I find an element $x\not\in\mathfrak mM_{\mathfrak m}$ for every maximal ideal $\mathfrak m$
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?