$\mathbb{R}^3$ as a field
26764
Proving that $\mathbb R^3$ cannot be made into a real division algebra (and that extending complex multiplication would not work)
118288
Complex structure on $\mathbb S^1 \times \mathbb S^3$
26497
Take $\mathbb{R}$ as a vector space over $\mathbb{Q}$, then a basis for $\mathbb{R}$, then $|B|=2^{\aleph_0}$
73412
Splitting field of $x^6+x^3+1$ over $\mathbb{Q}$
13262
$\mathbb{R}P^4$ and $\mathbb{R}P^6$ do not admit fields of tangent $2$-planes
84148
Why is $\mathbb{R}^2$ not a subspace of $\mathbb{R}^3$?
79725
Fields of arbitrary cardinality
151425
Does $\mathbb{R}^n$ have a real vector space structure with dimension other than $n$?
84189
Is $\mathbb{C}$ equal to $\mathbb{R}^2$?
7011
Integral domain with fraction field equal to $\mathbb{R}$
138653
Is $\mathbb{R}$ a subspace of $\mathbb{R}^2$?
30401
Determining the structure of the quotient ring $\mathbb{Z}[x]/(x^2+3,p)$
78143
Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
723
Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
151735
$\mathbb{R}^3 \setminus A$ deformation retracts onto $S^1 \vee S^2$