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location Ann Arbor, MI
age 25
visits member for 4 years, 2 months
seen 2 hours ago

Grad student at Michigan.


1d
comment Noether normalization for $k[x]_{x}$
Yes, I was thinking about $k[x]_{(x)}$, which is not finitely generated.
1d
comment Noether normalization for $k[x]_{x}$
Noether normalization applies to finitely generated $k$-algebras. Is $k[x]_x$ finitely generated as a $k$-algebra?
Oct
15
reviewed Close Congruences in Algebra
Oct
15
reviewed Approve suggested edit on Is $[a, a)$ equal to $\{a\}$ or $\varnothing$?
Oct
14
comment Groups of order $pq$ without using Sylow theorems
@the8thone That fact is used in the last line. The product of two elements of order $p$ need not be of order $p^2$.
Oct
10
revised Let $G$ be a finite group. Show that $G$ is isomorphic to a subgroup of $S_n$ (symmetric group).
edited tags
Oct
5
revised $a^k \mid a^\ell \Leftrightarrow k\leq \ell$?
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Oct
5
revised Generalizing the Big Omega function to Integral Domains
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Oct
5
answered Generalizing the Big Omega function to Integral Domains
Oct
5
comment Generalizing the Big Omega function to Integral Domains
You could not (naively) extend the definition to a general integral domain. In $\mathbf{Z}[x_1, x_2, x_3, x_4, x_5]/(x_1 x_2 - x_3 x_4 x_5)$, $x_1 x_2 = x_3 x_4 x_5$ gives two decompositions of some element into a different number of irreducibles.
Oct
3
comment What is an advantage of taking Dummit&Foote definition for 'word'?
1 is defined to be the empty product. You need this for the free group over S to actually be a group (1 is your identity).
Sep
30
awarded  Explainer
Sep
24
revised The smallest positive integer that can be written in the form $72x+40y$
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Sep
23
revised Prove the following fraction is irreducible
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Aug
29
reviewed Approve suggested edit on Is there an injective function such that $f(x^2)-f^2(x)\ge \frac{1}{4}$?
Aug
10
awarded  Yearling
Jul
2
comment When is $M \times N$ contained in$ M \otimes_{R} N$.
Should be $M = N = 0$.
Jun
29
answered Express Norm Using Inner Product
Jun
6
comment For $a=\cos(2\pi/n)$, show that $[\mathbb{Q}(a):\mathbb{Q}] = \ldots$
If $\zeta = e^{2 \pi i / n}$, can you think of a way to express $a$ in terms of $\zeta$? Remembering the complex definition of cosine might be useful here...
May
28
comment Show $\mathbb{Q}(\zeta)$ does not contain $\sqrt{7}$
Yes, but I'm not sure what motivation there is to not use Galois theory. Since you originally had the algebraic-number-theory tag, you could use that 2 is unramified in $\mathbf{Q}(\zeta_7)$.