How to show $u \in R^{x} \implies u \in R[X]^{x}$ for integral domain $(R,+, \times)$
53661
Intuition surrounding units in $R[x]$
1020
Proving that $\mathbb{Z}[\sqrt{2}]$ is a Euclidean domain
71479
Is there some elementary proof of invariance of domain?
123024
A Noetherian integral domain is a UFD iff $(f):(g)$ is principal
131120
Proving an integral equation.
2129
Showing that the derivative operator is not bounded on $L^2 (\mathbb{R})$
141410
Injective integral domains are fields
45098
How do we prove the "lying over" property for integral extensions?
19072
$\int_{\mathbb R} |f(x)| dx < \infty \implies \int^{\infty}_{n} |f(x)| dx \to 0$ as $n \to \infty$?
40564
Prove that $u(x,t)=\int_{-\infty}^{\infty}c(w)e^{-iwx}e^{-kw^2t}dw\rightarrow 0$ if $x\rightarrow \infty$
23721
Prove that the Gaussian Integer's ring is a Euclidean domain
33645
Proving that an integral domain has at most two elements that satisfy the equation $x^2 = 1$.
17161
Can anyone make me understand in simple language why the second condition for being an Euclidean domain is superfluous?
121198
$W^{1,1}(\mathbb{R}^n)$ is not compactly embedded in $L^1(\mathbb{R}^n)$?
125680
Show that $(1+u) \log (1+u) - u \ge \frac{u^2}{2(1+u/3)} $
103308
Showing that $\nabla\times(\nabla\times\vec{A}) = \nabla(\nabla\cdot\vec{A})-\Delta\vec{A}$
46746
How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?