Given ring $F[X]/(X^2)$ why is the ideal (X) the unique maximal ideal of the ring
45684
Is quotient of a ring by a power of a maximal ideal local?
67237
Pull back image of maximal ideal under surjective ring homomorphism is maximal
110022
Showing prime and maximal ideal
27766
Comaximal ideals in a commutative ring
151829
Why are maximal ideals prime?
121750
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.
97605
Let $f$ be a surjective homomorphism. Prove that $\ker(f)$ is a maximal ideal
53367
In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
116000
Prove that prime ideals of a finite ring are maximal
69353
Show that a ring with only trivial right ideals is either a division ring or $|R|=p$ and $R^2=\{0\}$. Why would $R$ be finite?
36150
Ideal in a ring of continuous functions
46040
Preimage of maximal ideal is maximal (why is this answer wrong?)
89313
Maximal ideals of polynomial rings in infinitely many variables
80397
Show that this set of polynomials is ideal in F[x]
146334
Are there fields $F$ such that the rings $F[x]/(x^2)$ and $F[x]/(x^2-1)$ are isomorphic?
7833
Ideal and minimal polynomial