Is $R[x]$ never a field?
46254
Why can't the Polynomial Ring be a Field?
17926
Zero divisor in $R[x]$
61375
Meaning of $\mathbb{R}[x]$
121643
Why isn't the zero ring the field with one element?
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
133312
Are these polynomials irreducible in $\mathbb{Q}[x]$?
122121
Is there a vector space that cannot be an inner product space?
66272
Is there a common notion of $\mathbb{R}^n$, for non-integer $n$?
121361
Showing that $\lnot Q \lor (\lnot Q \land R) = \lnot Q$ without a truth table
18336
$x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible?
90071
Why don't we have an isomorphism between $R[x]$ and $ R[[x]]$?
152354
Why is an empty set not a terminal object in categories $\mathsf{Top}$ and $\mathsf{Sets}$?
4507
Localization of a ring which is not a domain
121076
Show $x^p-t$ has no root in the field $\mathbb{F}_p(t)$
112556
When is $F(\sqrt c)$ a field?
73573
image of polynomial map is not an algebraic set
146891
Why is $\{\emptyset\} \not = \emptyset$?