Prove $R \times R$ is NOT an integral domain
11259
Prove $R\times S$ is not an integral domain
90599
Trouble with proving $A$ is an integrally closed domain $\Rightarrow$ $A[t]$ is integrally closed domain
5250
Are $T\mathbb{S}^2$ and $\mathbb{S}^2 \times \mathbb{R}^2$ different?
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
32917
Show that, for $t>0$, $\log t$ is not a polynomial.
4507
Localization of a ring which is not a domain
62951
Is there a more direct way of proving that this ring is an integral domain?
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
12189
Prove norm doesn't come from inner product.
69611
If $R$ and $S$ are rings then $R \times S$ is never a field
7828
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
71479
Is there some elementary proof of invariance of domain?
107389
Show that the vector space of real functions is not finitely spanned
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
86234
Explain why $\mathbb{Z \times Z}$ and $\mathbb{R \times R}$ is not a field
96132
$R$ integral domain : $u\in R^*, a \text{ is prime} \iff au \text{ is prime}$
42170
$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element