$\mathbb{Z}$ is not an algebra over a field
57310
Prove $\mathbb{Z}$ is not a vector space over a field
66313
$\mathbb{Z}[i]/(a+bi) \cong \mathbb{Z}_{a^2+b^2}$ if $(a,b)=1$
53335
Why isn't $\mathbb{C}[x,y,z]/(xz-y)$ a flat $\mathbb{C}[x,y]$-module
14003
$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
101164
Show that $B \cong \mathbb Z /2\mathbb Z$ for a Boolean field B
73573
image of polynomial map is not an algebraic set
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
12110
How are $2\mathbb{Z}\ncong3\mathbb{Z}$ different as rings?
70576
Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
17991
Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
37904
Prove that the multiplicative groups $\mathbb{R} - \{0\}$ and $\mathbb{C} - \{0\}$ are not isomorphic.
92298
The additive group $\mathbb{G}_a$ over an infinite field $k$ is not a topological group
81982
Is $\mathbb{Z}[x]$ a principal ideal domain?
67796
How to prove that the algebra $k[x, xy, xy^2, xy^3, \dotsc]$ is not finitely generated?
86234
Explain why $\mathbb{Z \times Z}$ and $\mathbb{R \times R}$ is not a field
19310
Identify the ring $\mathbb{Z}[x]/(2x)$