Let $ D $ be an Euclidean domain and $d$ be the associated function. $u$ is a unit in $D$ if and only if $d(u)=d(1)$
54957
The necessary and sufficient condition for a unit element in Euclidean Domain
9355
If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
8317
Understanding a proof of "If $R$ is an integral domain, then $R[x]$ is an integral domain as well".
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
67485
The ratio $\frac{u(z_2)}{u(z_1)}$ for positive harmonic functions is uniformly bounded on compact sets
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
90599
Trouble with proving $A$ is an integrally closed domain $\Rightarrow$ $A[t]$ is integrally closed domain
14158
Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
64172
Show that if $f$ is analytic in a domain $D$ and $|f(z)|$ is constant in $D$, then the function $f(z)$ is constant in $D$
149634
$ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
121359
Show that $d_b(x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric.
19599
$ d(x_n,y_n) \to d(x,y)$ if $x_n\to x$ and $y_n \to y$
82458
Homeomorphism between the unit disc and the unit square
114047
Metric $d(x,y)=\frac{|x-y|}{\sqrt{1+x^2}\sqrt{1+y^2}}$ on $\mathbb{R}$
113696
Showing that the unit ball in $(C^\alpha[a, b], \|\cdot\|_\alpha)$ is compact in $(C[a, b], \|\cdot\|_\infty)$
127436
Conformal Maps onto the Unit Disc in $\mathbb{C}$
83798
Does $A$ a UFD imply that  $A[T]$ is also a UFD?