If $F$ is a field show that $F[x]$ is not a field.
46254
Why can't the Polynomial Ring be a Field?
57310
Prove $\mathbb{Z}$ is not a vector space over a field
136842
$|x-f(x)|<5777$, Show that $f$ is surjective
140106
How to prove a finite field is not ordered?
39583
ii) Show that $u$ is not a real part of the function which analytic on $\mathbb{C} \backslash \lbrace 0 \rbrace$
85092
Proving $ f(x) = x^2 $ is not uniformly continuous on the real line
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
14994
Showing a function $f$ cannot be surjective
82485
Show that the set of non zero rationals is not a cyclic group under multiplication.
35953
Prove that a function is not injective
125043
Show that F(A−B) is not necessarily a subset of F(A)−F(B).
83595
Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension
152841
I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.
58424
If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field.
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
121076
Show $x^p-t$ has no root in the field $\mathbb{F}_p(t)$
41810
Should all polynomial functions from F to F (F is a field) have coefficients in F?