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Hailie Mathieson's user avatar
Hailie Mathieson's user avatar
Hailie Mathieson's user avatar
Hailie Mathieson
  • Member for 12 years, 2 months
  • Last seen more than 5 years ago
29 votes
2 answers
5k views

Examples proving why the tensor product does not distribute over direct products.

13 votes
2 answers
580 views

Why is it that $\det(\phi-x\text{id})=\sum_{i=0}^n (-1)^ic_ix^i$?

13 votes
3 answers
2k views

If $\operatorname{Hom}(X,-)$ and $\operatorname{Hom}(Y,-)$ are isomorphic, why are $X$ and $Y$ isomorphic?

11 votes
1 answer
1k views

Center of Weyl algebra over a field of characterstic $0$?

10 votes
1 answer
6k views

Existence of irreducible polynomial of arbitrary degree over finite field without use of primitive element theorem?

9 votes
1 answer
3k views

Do $T$-invariant subspaces necessarily have a $T$-invariant complement?

8 votes
2 answers
1k views

Is this quotient ring $\mathbb{C}[z_{ij}]/\ker\phi$ integrally closed?

7 votes
1 answer
310 views

Why is the kernel of this strange polynomial homomorphism what it is?

7 votes
2 answers
2k views

How to find the nilpotent elements of $\mathbb{Z}/(\prod p_i^{n_i})$?

6 votes
4 answers
2k views

If $a^m=b^m$ and $a^n=b^n$ for $(m,n)=1$, does $a=b$? [duplicate]

6 votes
2 answers
502 views

Why does $(2/p)=\prod_{k=1}^{(p-1)/2}2\cos\left(\frac{2\pi k}{p}\right)$?

5 votes
2 answers
660 views

If $A\equiv 1\pmod{3}$, then $4p=A^2+27B^2$ uniquely determines $A$.

4 votes
2 answers
328 views

On Hatcher's proof that $H_0(X)$ is a direct sum of $\mathbb{Z}$s?

4 votes
2 answers
331 views

Can $\operatorname{Spec}(R[X])$ ever be finite?

4 votes
1 answer
108 views

Weight $\mathfrak{sl}_2$-module with finite dimensional weight spaces has finite length?

4 votes
1 answer
129 views

Understanding weight spaces of weight module from its composition factors?

4 votes
1 answer
1k views

Theorem of Kaplansky, $R$ is a division ring if every element but one is (right) quasi-invertible.

4 votes
1 answer
3k views

Why does $k[X,Y]/(XY)$ have two minimal primes?

4 votes
1 answer
718 views

Change of base property for flat modules?

4 votes
0 answers
156 views

Reading string diagram for counit-unit triangle identities?

3 votes
0 answers
60 views

If $F$ and $G$ are adjoint functors, why are $\operatorname{Nat}(G,G)\simeq\operatorname{Nat}(F,F)$ as algebras? [duplicate]

3 votes
2 answers
502 views

Why is the kernel of $k[x_1,\dots,x_n]\to k$ a maximal ideal?

3 votes
1 answer
300 views

Troubling calculation for a wreath product of groups.

3 votes
1 answer
299 views

Determining the sign of the Gauss sum under the change of variable $x\mapsto 1+u$.

3 votes
1 answer
637 views

Why is the cyclic decomposition of a primary torsion module not unique?

3 votes
2 answers
141 views

Does $\exp(\ln(I+A))=I+A$ when $\|A\|<1$?

2 votes
1 answer
204 views

If $f\colon X\to S^k$ smooth, $X$ compact and $Z\subseteq S^k$ closed, then $I_2(f,Z)=0$.

2 votes
1 answer
240 views

Vector bundles on $\mathbb{A}^1_k$ with doubled origin?

2 votes
0 answers
89 views

Why are $\mathfrak{pgl}_n\simeq\mathfrak{sl}_n$ when characteristic does not divide $n$?

2 votes
1 answer
82 views

Uniqueness up to sign of $L$ and $M$ in $p=\frac{1}{4}(L^2+27M^2)$.