Let $R$ be a commutative, unital ring and let $I$ be an ideal of $R.$ Prove that if $I$ is maximal then $R/I$ is a field.
138130
If $I$ is a maximal ideal of $R$, why is $R/I$ a field?
110984
Ideals and prime ideals in a commutative ring.
112150
Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
74559
$A$ and $B$ are ideals of a ring ${R}$ such that $A\cap B=\{0\}$. Prove that $st=0$ for every $s\in A, t\in B$.
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
129371
Maximal ideals in the ring of real functions on $[0,1]$
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 $I=(0)$?
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
29126
Maximal ideal in the ring of continuous functions from $\mathbb{R} \to \mathbb{R}$
116883
About ideals in a ring which is a $k$ vector space
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
43230
Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
116000
Prove that prime ideals of a finite ring are maximal
18406
An ideal whose radical is maximal is primary
27766
Comaximal ideals in a commutative ring
87078
Prove the following set is an ideal of the ring $Z[x]$
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.