$R$ - commutative ring. $I$ - ideal of that ring. Prove that ring $R/I$ - is a field
131943
How to directly prove that $M$ is maximal ideal of $A$ iff $A/M$ is a field?
111307
If ideal $I$ of domain $R$ is free $R$-module, then $I$ is principal ideal.
150911
Prove that the ring is Artinian and find a composition series of ideals
37393
$R$ is commutative, $I$,$J$ are ideals, $I+J=R$, then $IJ=I\cap J$
87078
Prove the following set is an ideal of the ring $Z[x]$
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
87103
Quick question about ideals of field $F$ in $F[x]$ are principal.
77862
Question about fields and quotients of polynomial rings
19112
Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
138752
Prove the Radical of an Ideal is an Ideal
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 $I=(0)$?
99567
Proving that an inverse ring homomorphism of an ideal is an ideal?
40705
If $M$ is an $R$-module and $I\subseteq\mathrm{Ann}(M)$ an ideal, then $M$ has a structure of $R/I$-module
155745
Ideals of $\mathbb{Z}[X]$
69373
Prove that $(0)$ is a radical ideal in $\mathbb{Z}/n\mathbb{Z}$ iff $n$ is square free
16643
A slick proof that a field which is finitely generated as a ring is finite