If in a commutative ring $R$ a maximal ideal is nilpotent, then $R$ is local
139794
In a (not necessarily commutative) ring, a nilpotent maximal ideal is unique.
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?
42552
Localisation is isomorphic to a quotient of polynomial ring
156443
if $x$ and $y$ commute with $[x y]$, then $[x y]$ is nilpotent
112150
Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
114343
If $I$ and $J$ are ideals in a ring $R$ with $1$ such that $I+J = R$, show that $I^m$ and $J^n$ are co-maximal for all $m,n \in \mathbb{N}$
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
93723
Find all the maximal ideals in the ring $\mathbb{R}[x]$.
30714
A question on ring homomorphisms and maximal ideals.
111189
Intersection of all maximal ideals containing a given ideal
96144
Every element outside the maximal ideal of a local ring is a unit
74259
Why is the localization of a commutative Noetherian ring still Noetherian?
149412
Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
138130
If $I$ is a maximal ideal of $R$, why is $R/I$ a field?
66968
if $a,b$ are nilpotent elements of a commutative ring $R$, show that $a+b$ is also nilpotent
73689
A question about the equivalence relation on the localization of a ring.
104782
Polynomial irreducible - maximal ideal