15,657 reputation
12042
bio website math.brown.edu/~lubinj
location Minnesota
age 78
visits member for 3 years, 3 months
seen 8 hours ago

Aged mathematician


Jan
23
comment Soft question: Union of infinitely many closed sets
just what I was about to say.
Jan
22
comment Can interior set or exterior set be empty?
You need examples. Think of $\Bbb Q\subset\Bbb R$.
Jan
22
comment $\dfrac{\mathbb{Z}[x]}{(x^2 +5)}$ is isomorphic to $\mathbb{Z}[\sqrt{-5}]$
Yes, but… Isn’t the fact that $x^2+5$ is monic part of the story? This is what makes Euclidean division by $x^2+5$ work within $\Bbb Z[x]$. The only way I can see how to know that $g$ has integer coefficients is by using Euc. div. Am I being foolish here?
Jan
21
comment Efficient Method/Algorithm to Compute the P-adic Ordinal of a Positive Integer
Your conjecture is on the mark. Good luck!
Jan
21
answered Efficient Method/Algorithm to Compute the P-adic Ordinal of a Positive Integer
Jan
20
answered To intermediate field is Galois$\iff$ Galois group over intermediate field is a normal subgroup
Jan
20
comment To intermediate field is Galois$\iff$ Galois group over intermediate field is a normal subgroup
Not likely that a text by Artin has anything wrong with it (he says, worshipfully).
Jan
20
comment How many $n$th roots does $0$ have?
Something trivial, trifling, or of little importance. If I had thought otherwise, I would have given my own answer.
Jan
20
comment How many $n$th roots does $0$ have?
This must be the first time I disagree with you. OP didn’t ask for the roots of $X^n$, but the $n$-th roots of zero. Not the same thing, I would say. But to spend time on the distinction seems to me nugatory.
Jan
19
comment To intermediate field is Galois$\iff$ Galois group over intermediate field is a normal subgroup
Is this an exercise from the text? If $F_2\supset F_0$ wasn’t Galois to start with, do you have a definition of $\text{Gal}(F_2/F_0)$?
Jan
19
comment Determine whether $ \{ a + b \sqrt[3]{2} + c\sqrt[3]{4} \mid a,b,c\in\mathbb Z\}$ is an abelian group
Right you are. But alternatively, one may choose simply to show that the set is closed under subtraction.
Jan
19
revised If $x^2+x+1=0 $, then find the value of $(x^3+1/x^3)^3$?
corrected an embarrassing and misleading typo
Jan
19
comment If $x^2+x+1=0 $, then find the value of $(x^3+1/x^3)^3$?
@Galc127, or course, thanks for spotting the embarrassing sloppiness on my part.
Jan
19
answered If $x^2+x+1=0 $, then find the value of $(x^3+1/x^3)^3$?
Jan
19
awarded  Excavator
Jan
19
comment Laurent series for $\frac1{z^2+1}$
Gerry, he’s asking for a series valid outside the unit circle, so in $1/z$.
Jan
19
revised Laurent series for $\frac1{z^2+1}$
There was a topo in the numerator of the outside factor of the last sum. I’ve cofrrected it. —Lubin
Jan
19
comment Laurent series for $\frac1{z^2+1}$
Well, I do apologize for not noticing that the other answer has (had, before my edit) a typo, putting $2z-1$ in the numerator instead of $2z-4$. Otherwise, it really looks blameless to me.
Jan
19
comment Laurent series for $\frac1{z^2+1}$
You’ve said that the other answer is incorrect. That involves showing that the two answers actually are different.
Jan
19
comment Laurent series for $\frac1{z^2+1}$
Can you show us. for some positive $n$, a coefficient of $z^{-n}$ in your formula that’s different from the corresponding coefficient in the other answer?