examples such that (i)$F[x]$ is not a field, (ii) $F[x]$ is also a field.
46254
Why can't the Polynomial Ring be a Field?
19996
Example where union of increasing sigma algebras is not a sigma algebra
15128
Example of non-decomposable ideal
98577
Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
42774
Examples of involutions on $\mathbb{R}$
79450
For field extensions $F\subsetneq K \subset F(x)$, $x$ is algebraic over $K$
1440
Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$
22750
What are examples of functions that are $L^1$ but not $L^2$ and vice versa?
14994
Showing a function $f$ cannot be surjective
10111
Prove or disprove that Q[√2] is a field
6646
A (non-artificial) example of a ring without maximal ideals
131460
Example of finite field extension where root not separable
86234
Explain why $\mathbb{Z \times Z}$ and $\mathbb{R \times R}$ is not a field
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
63701
An example of a regular function over an open set
146480
Example of $\deg(fg)<\deg(f)+\deg(g)$
140106
How to prove a finite field is not ordered?