Intereting Posts

Normal and central subgroups of finite $p$-groups
Using Ratio test/Comparison test
Linear basis of sum of kernels of two linear applications from $\mathbb R^4$ to $\mathbb R^2$
Suppose that half of the elements of G have order 2 and the other half form a subgroup H of order n. Prove that H is an abelian subgroup of G.
The contradiction method used to prove that the square root of a prime is irrational
Let $A_1,A_2,..,A_n$ be the vertices of n sides of a regular polygon such that $1/A_1.1/A_2=1/A_1.1/A_3+1/A_1.1/A_4$ then value of $n$ must be?
Is the product of two non-holomorphic function always non-holomorphic?
Determine the minimal polynomial of $\sqrt 3+\sqrt 5$
If $M$ is an $R$-module and $I\subseteq\mathrm{Ann}(M)$ an ideal, then $M$ has a structure of $R/I$-module
Inverse of a block matrix
Existence of right inverse.
Computing the order of elements in Dihedral Groups
When is an operator on $\ell_1$ the dual of an operator on $c_0$?
Why is the Fejér Kernel always non-negative?
Quasi-interactive proof on real numbers

Let $\mathcal{O}$ be a Dedekind domain, $K$ its field of fractions. Suppose $f\in \mathcal{O}[X]$ is irreducible. Is it irreducible in $K[X]$?

The motivation for my question is that this is true for UFD’s, so it is natural to ask if it is still valid over an arbitrary Dedekind domain.

- Nice proof for finite of degree one implies isomorphism?
- The action of a Galois group on a prime ideal in a Dedekind domain
- What is the kernel of $K \to K$, defined by $T \mapsto x$?
- Localization at a prime ideal is a reduced ring
- Is the image of a tensor product equal to the tensor product of the images?
- Projectivity of $B$ over $C$, given $A \subset C \subset B$

- Show that $\left\langle\alpha_A(I\cap J)\right\rangle \subset \left\langle\alpha_A(I)\right\rangle \cap \left\langle\alpha_A(J)\right\rangle $.
- Generators for the radical of an ideal
- The kernel of $R \to A \otimes_R B$ is nil
- About some characterizations of Prufer domains
- $\mathbb{Q}/\langle x^2+y^2-1 \rangle$ is an integral domain, and its field of fractions is isomorphic to $\mathbb Q(t)$
- Why does flatness imply these Homs are isomorphic?
- Could I see that the tensor product is right-exact using its universal property and the Yoneda lemma?
- Nilradical strictly smaller than Jacobson radical.
- Do localization and completion commute?
- Example of non-Noetherian non-UFD Krull domain?

This has been answered pretty exhaustively by Pete Clark on MO. The upshot is that as soon as the class number is not 1, the result does not hold.

- Find a point position on a rotated rectangle
- Do we have to define natural numbers in geometry?
- Asymptotic integral expansion of $\int_0^{\infty} t^{3/4}e^{-x(t^2+2t^4)}dt$ for $x \to \infty$
- My sister absolutely refuses to learn math
- Find shortest distance between lines in 3D
- Is there an uncountable proper sub-field of $\mathbf{R}$?
- How to compute $\int_0^\infty e^{-a(s^2+1/s^2)}\, ds$
- Weakly Harmonic Functions (Weak Solutions to Laplace's Equation $\Delta u=0$) and Logic of Test Function Techniques.
- In a finitely generated $k$-algebra, the nilradical is $0$ iff the Jacobson radical is $0$.
- Continued fraction of a square root
- Long exact sequence into short exact sequences
- about weak derivative of Bochner integrable function
- Stolz-Cesàro Theorem
- Isometry group of a norm is always contained in some Isometry group of an inner product?
- Given $a,b,c$ are the sides of a triangle. Prove that $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$