How to show that ${\Bbb Q}[x,y]/(x^2+y^2+1)$ is a PID?
121845
Quotient of polynomials, PID but not Euclidean domain?
113152
Prove Principal Ideal Domain from Bezout's condition, and terminating divisibility chain
81671
Proof of identity $\sqrt {xy} = \sqrt x \sqrt y$ for $x,y \in \mathbb R^+$
125030
Prove that $\det(A)=p_1p_2-ba={bf(a)-af(b)\over b-a}$
13174
Show that $A[X]/(aX+b)$ is an integral domain
105973
how do we know the BBP formula for $\pi$ is valid?
12764
$\Bbb RP^2$ as the union of a Möbius band and a disc
58416
Valuations on $\Bbb Q(t)$
77464
Prove that ${x dy - y d x\over x^2 + y^2}$ is not exact
118299
Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
131881
Show that the roots of P' lie in the same half plane as the roots of P
6984
Inverting $a+b\sqrt{2}$ in the field $\Bbb Q(\sqrt{2})$
33944
Describe $\mathbb{R}[x]/(x^{2}+ax+b)$ where $a,b \in \mathbb{R}$
31451
Proving a subring of $\mathbb{Q}$ containing $\mathbb{Z}$ is a PID
1914
General way to determine $\mathbb{Q}(\gamma) = \mathbb{Q}(\alpha,\beta)$ given $\alpha$ and $\beta$
141477
Decomposition of finitely generated graded modules over PID
27629
How to prove that $S^{2n+1}/S^1$ is homeomorphic to $\mathbb CP^n$ under a given identification