Disproving that $\mathbb R[x]$ is a field
46254
Why can't the Polynomial Ring be a Field?
93017
Isomorphism between $\Bbb R$ and $\Bbb R(X)$?
61375
Meaning of $\mathbb{R}[x]$
27021
Show that $Q[\sqrt3]$ is a field
48962
Show the two fields are not isomorphic
57310
Prove $\mathbb{Z}$ is not a vector space over a field
121076
Show $x^p-t$ has no root in the field $\mathbb{F}_p(t)$
26749
$\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
136770
Any field that contains the integers contains the rationals as a subfield (Analysis proof)
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
55026
$\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
29635
Fields finitely generated as $\mathbb Z$-algebras are finite?
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$