How can we show that $I$ is an ideal?
87382
Non-invertible elements form an ideal
47134
Ideals generated by two elements
63447
Prove that the kernel of a homomorphism is a principal ideal. (Artin, Exercise 9.13)
69649
If an ideal contains the multiplicative identity, then it is the whole ring
116883
About ideals in a ring which is a $k$ vector space
70320
Let $R$ be a commutative Noetherian ring (with unity), and let $I$ be an ideal of $R$ such that $R/I \cong R$. Then is $I=(0)$?
87078
Prove the following set is an ideal of the ring $Z[x]$
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
72640
$(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
148208
In Noetherian ring $R$, ideal $I\subset R$, $P\in\mathrm{Ass}(I),P=I:a$ for some $a\in R$.
18186
Prove that ideal $I = \langle X^2,X+1\rangle$ is principal or not (in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$ )
101320
How to tell $i$ from $-i$?
138752
Prove the Radical of an Ideal is an Ideal
104784
On the grade of an ideal
69012
How to directly prove every element in a ring with exactly three ideals is either a unit or a zero divisor?
29019
Ideals in direct product of rings