Show that the ideal generated by $13$ and $x^2 − x + 1$ in $\mathbb Z[x]$ is not maximal.
37929
Classification of prime ideals of $\mathbb{Z}[X]$
144572
Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma
112150
Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
124864
A not free $\mathbb{Z}$-module
18186
Prove that ideal $I = \langle X^2,X+1\rangle$ is principal or not (in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$ )
113582
How can I find an element $x\not\in\mathfrak mM_{\mathfrak m}$ for every maximal ideal $\mathfrak m$
43774
Given distinct maximal ideals $M_1,...,M_n$, is $M_1\cdots M_n$ radical?
6699
An ideal that is maximal among non-finitely generated ideals is prime.
138130
If $I$ is a maximal ideal of $R$, why is $R/I$ a field?
74537
Maximal Ideals in $K[y]$
18406
An ideal whose radical is maximal is primary
33245
Show that every ideal of the ring $\mathbb Z$ is principal
92703
Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.
144623
Can one avoid AC in the proof that in Noetherian rings there is a maximal element for each set?
69352
Prove that $I= \{a+bi \in ℤ[i] : a≡b \pmod{2}\}$ is an maximal ideal of $ℤ[i]$.
80232
Suppose that R is a commutative ring with unity such that for each $a$ in $R$ there is an integer $n > 1\mid a^n =a$. Every prime ideal is maximal?
19230
Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$