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Apr
30
comment Polynomial roots in the ring extension
The issue with the polynomial ring $R[x]$ is that $x$ commutes with elements of $R$, and there is no reason a root of $f$ should commute with $R$. Would it work to start with the free non-commutative algebra in one generator over $R$ (I think we can construct this as the set of finite sums of elements $r_1 x^{n_1}\ldots r_k x^{n_k}$, modulo the necessary relations), and quotient by the two-sided ideal generated by $f(x)$?
Apr
30
answered Books about harmonic numbers
Apr
30
answered Denominators of harmonic numbers: asymptotic behaviour.
Apr
29
awarded  Nice Answer
Apr
25
awarded  Pundit
Apr
23
comment Are we allowed to compare infinities?
The OP's question was not specifically about cardinality. The question is about comparing infinities, and there are several ways to do this.
Apr
23
comment Are we allowed to compare infinities?
Comparing densities is a natural way to compare sizes of infinite sets of integers.
Apr
22
answered Are we allowed to compare infinities?
Apr
11
answered A closed form for a lot of integrals on the logarithm
Apr
7
comment Which functions can be the resistance of a network?
I intended that you only have one copy of each unknown resistor, but I am also interested in what happens if you have more than one.
Apr
7
asked Which functions can be the resistance of a network?
Apr
5
awarded  Yearling
Mar
30
comment Can we rediscover the category of finite (abelian) groups from its morphisms?
I answered the linked question, for every $\sigma\in\widehat{\mathbb{Z}}$, we can define an automorphism $F_\sigma$ of the category of finite groups, taking $(G,\circ)$ to $(G,\circ^\sigma)$, where $x\circ^\sigma y:=(x^\sigma y^\sigma)^{\sigma^{-1}}$. All of these are isomorphic to the identity, though, so they don't give a counterexample to this question.
Mar
30
awarded  Revival
Mar
30
answered Cogroup structures on the profinite completion of the integers
Mar
30
comment Is torsion of a topological module closed?
Crossposted at mathoverflow. I posted an answer there.
Mar
25
comment Infinite primes (places) of a number field geometrically
What you're asking for may be difficult because any $\mathrm{Spec}(\mathcal{O}_K)$ is already proper over $\mathrm{Spec}(\mathbb{Z})$ (it is finite). In particular, every map from $\mathrm{Spec}(\mathcal{O}_K)$ to a scheme that is separated over $\mathbb{Z}$ has closed image, so in particular no separated scheme can have $\mathrm{Spec}(\mathcal{O}_K)$ as a non-trivial dense open subset.
Mar
2
answered Integral $I=\int \frac{dx}{(x^2+1)\sqrt{x^2-4}} $
Feb
29
reviewed Approve Is this statement true: a set is open if every point has a closed ball contained inside of the set
Feb
26
awarded  Nice Answer