Preimage of maximal ideal is maximal
30714
A question on ring homomorphisms and maximal ideals.
136654
$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$
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 $m,n \in \mathbb{N}$
116000
Prove that prime ideals of a finite ring are maximal
151829
Why are maximal ideals prime?
49521
In an extension of finitely generated $k$-algebras the contraction of a maximal ideal is also maximal
117786
Show that some monomial ideal is primary
7833
Ideal and minimal polynomial
87780
Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
68202
Must an ideal generated by an irreducible element be a maximal ideal?
113582
How can I find an element $x\not\in\mathfrak mM_{\mathfrak m}$ for every maximal ideal $\mathfrak m$
99715
Proper ideal and units proof
116430
If $I = \langle 2\rangle$, why is $I[x]$ not a maximal ideal of $\mathbb Z[x]$, even though $I$ is a maximal ideal of $\mathbb Z$?
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.
138168
Prove: The pre-image of an ideal is an ideal.
93723
Find all the maximal ideals in the ring $\mathbb{R}[x]$.
114193
On the absolute norm of an ideal