Proving the ideal $I=\{f(x)\in\mathbb{Z}[x] | f(0)$ is even$\}$ is not principal in the ring $R=\mathbb{Z}[x]$
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
84663
$A$ local Noetherian ring with principal maximal ideal implies PIR?
110984
Ideals and prime ideals in a commutative ring.
22544
Let R be a commutative ring, and let P be a prime ideal of R. Suppose that P has no nontrivial zero divisors in it. Show that R is an integral domain.
33576
Non-principal ideal in $K[x,y]$?
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
69649
If an ideal contains the multiplicative identity, then it is the whole ring
99423
Is it true every ideal of $\mathbb{Z}[x]$ is finitely generated?
146801
Primary decomposition of an ideal
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?
129371
Maximal ideals in the ring of real functions on $[0,1]$
69373
Prove that $(0)$ is a radical ideal in $\mathbb{Z}/n\mathbb{Z}$ iff $n$ is square free
90314
Maximal ideals in $R[x]$
117786
Show that some monomial ideal is primary
40705
If $M$ is an $R$-module and $I\subseteq\mathrm{Ann}(M)$ an ideal, then $M$ has a structure of $R/I$-module
133975
Localising a polynomial ring and non-maximal prime ideal
81982
Is $\mathbb{Z}[x]$ a principal ideal domain?