106 reputation
516
bio website
location
age
visits member for 2 years, 8 months
seen 20 hours ago

Apr
17
asked Equivalence of two characterizations of the norm of an algebraic integer.
Apr
16
asked Finding a matrix with determinant $1$ subject to some loose conditions.
Apr
15
comment Proving a set is uncountable
Hopefully one of the 4 answers will help you along. Wait long enough and there may be 10.
Apr
15
answered Proving a set is uncountable
Apr
15
comment A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.
thanks for the catch, fixed
Apr
15
revised A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.
deleted 6 characters in body
Apr
15
accepted Two questions about integral “splitting ring” extensions
Apr
15
revised A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.
made the question more general
Apr
15
asked A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.
Apr
11
comment Is there a computer program that does diagram chases?
On the other hand even a program that only handled certain classes of diagrams would be of great practical use.
Apr
11
comment Two questions about integral “splitting ring” extensions
I see what you're getting at, maybe. Are you suggesting that (a) is unnecessary to prove (b)? I think the integral case might be equivalent to the non-integral case provided our $f$ and $g$ both split in some integral ring extension.
Apr
11
comment Two questions about integral “splitting ring” extensions
Why does it suffice to show that this is true for one polynomial? Unless I made a mistake I have already shown that this is true. Where do my (a) and (b) fit in this answer?
Apr
11
accepted Extending a set of complex Borel measures defined on subsets to the whole space
Apr
11
comment Two questions about integral “splitting ring” extensions
Thank you! Fixed.
Apr
11
revised Two questions about integral “splitting ring” extensions
fixed typo
Apr
11
comment Eigenvalues of matrices.
As David said, this is false. But since you do know that the product of the eigenvalues of a square matrix is the determinant, the fact that the determinant is multiplicative gives you some information about the original eigenvalues.
Apr
11
asked Two questions about integral “splitting ring” extensions
Mar
26
accepted Understanding why the positive bounded linear functionals on $C_0(X)$ are given by integration against finite Radon measures.
Mar
26
comment Counterexamples in convergence in $M(X)$ and $C_0(X)$.
I was taking the definition straight out of Folland of total variation. Can you be specific where you think I messed up?
Mar
26
comment Counterexamples in convergence in $M(X)$ and $C_0(X)$.
The total variation of a complex Radon measure is the positive measure $|\nu|$, where $d|\nu|=|f| d\mu$ for $\mu$ a positive measure, where by the Riesz Representation theorem $f$ is in $C_0(X)$. So if $\mu_n=\delta_n\to 0$ as $n\to\infty$, s.t. $|\mu_\alpha|(X)\to |\mu|(X)$ this means that for some $f\in C_0(X)$, $f(n)=|\mu_\alpha|=\int |f_\alpha|\ d\mu \nrightarrow \int |f|\ d\mu=|\mu|(X)=0$, but $\delta_n\to 0$ vaguely since for all $f\in C_0(X)$ for $n$ large $\int f\mu_n$ is small. How is that?