Z[x] is not isomorphic to Q[x] as a rings
92703
Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.
121465
$R[x]$ has a subring isomorphic to $R$.
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
9794
Quotient ring of Gaussian integers $\mathbb{Z}[i]/(a+bi)$ when $a$ and $b$ are NOT coprime
158502
Showing $\sin(\bar{z})$ is not analytic at any point of $\mathbb{C}$
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
112933
Show that $Z\times Z$ is not cyclic...
47114
What is necessary and/or sufficient for polynomials to provide isomorphic quotient rings?
108044
Isomorphic extensions of $\mathbb Z_3$ by $\mathbb Z_3 \times \mathbb Z_3$ which are not equivalent
86542
Group of positive rationals under multiplication not isomorphic to group of rationals
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
140557
Counting ring homomorphisms from $\mathbb{Z}[x,y]/(x^3+y^2-1)$ to $\mathbb{Z_7}$
37904
Prove that the multiplicative groups $\mathbb{R} - \{0\}$ and $\mathbb{C} - \{0\}$ are not isomorphic.
152297
Understanding quotients of $\mathbb{Q}[x]$
85987
Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain