Show that if $F$ is a field, $f(x) \in F[x]$, then $f(x) * F[x]$ is an ideal in $F[x]$, and every ideal of $F[x]$ is of this form.
89271
If $F$ is a field, then $F[x]$ is a principal ideal domain proof question
131943
How to directly prove that $M$ is maximal ideal of $A$ iff $A/M$ is a field?
7567
Degree of Field Extensions and $F(\alpha)$
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
119305
Is the splitting field equal to the quotient $k[x]/(f(x))$ for finite fields?
118306
$I:=\{f(x)\in R\mid f(1)=0\}$ is a maximal ideal?
81296
If A and B are ideals of a ring, show that A + B = $\{a+b|a \in A, b \in B\}$ is an ideal
146334
Are there fields $F$ such that the rings $F[x]/(x^2)$ and $F[x]/(x^2-1)$ are isomorphic?
79450
For field extensions $F\subsetneq K \subset F(x)$, $x$ is algebraic over $K$
129597
Is a field perfect iff the primitive element theorem holds for all extensions, and what about function fields
38963
Ideals in ring of continuous functions $\mathcal{C}[0,1]$ ... NBHM- Algebra
111444
Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
36150
Ideal in a ring of continuous functions
69373
Prove that $(0)$ is a radical ideal in $\mathbb{Z}/n\mathbb{Z}$ iff $n$ is square free
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
587
Ideal Generated by the Union of Two Ideals