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Michael Morrow
  • Member for 2 years, 6 months
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6 votes
1 answer
325 views

Show $\sqrt[3]{5}$ is not contained in any cyclotomic extension of $\mathbb{Q}$.

5 votes
1 answer
75 views

Let $|G|=2^np$, $p$ an odd prime, $H\unlhd G$ a Sylow $2$-subgroup with $H\cong(\Bbb{Z}/2\Bbb{Z})^n$, $p\nmid 2^n-1$. Prove $Z(G)$ is nontrivial.

4 votes
2 answers
207 views

Subspace of polynomials vanishing to order $n$

4 votes
0 answers
68 views

Find all ring maps $\mathbb{Q}[x]/(x^{101}+2)\longrightarrow\mathbb{Q}[x]/(x^{501}-2)$

4 votes
3 answers
90 views

Roots of $x^{p^{n-1}}+\ldots+x^p+x$ in $\mathbb{F}_{p^n}$

4 votes
1 answer
98 views

Is the space $\text{Map}(S^1,S^1)$ of continuous maps on $S^1$ compact? (Compact-open topology)

3 votes
1 answer
77 views

Any two components of a topological group are homeomorphic

3 votes
1 answer
162 views

Can the Klein bottle cover the torus? Show the Klein bottle can't be covered by a space $X$ with $\pi_1(X)=\mathbb{Z}/3\mathbb{Z}$.

3 votes
3 answers
104 views

Subgroups of $C_2\times C_6$

3 votes
2 answers
86 views

Show $y^3+xy+x^2(x-1)^2\in\mathbb{R}[x,y]$ is irreducible

3 votes
1 answer
104 views

Integral of function equals integral of measure - Tonelli's Theorem

3 votes
1 answer
129 views

Odd-dimensional $\mathbb{R}$-vector space has a one-dimensional $\varphi$-invariant subspace

3 votes
1 answer
415 views

Prove quotient of graded ring with graded ideal is a graded ring

2 votes
1 answer
527 views

Minimal Gröbner bases have the same leading terms

2 votes
0 answers
61 views

Classification of monomials in a monomial ideal

2 votes
2 answers
102 views

Two questions about graded rings

2 votes
0 answers
51 views

Your favorite way to think of $k[x_1,\ldots,x_n]$ modulo some graded ideal?

2 votes
2 answers
80 views

Equivalent properties of graded ideals

2 votes
2 answers
307 views

Restriction of surjective linear map is isomorphism

2 votes
1 answer
183 views

Non-trivial normal subgroup of $G$ intersects the center $Z(G)$ non-trivially

2 votes
1 answer
41 views

Automorphism of vector space $V$ such that $\varphi(S_1)=S_2$

2 votes
1 answer
444 views

How to find generators for the subfields of $\mathbb{Q}(\zeta_{12})$

2 votes
2 answers
47 views

Minimal polynomial of $\varphi:g+(f)\mapsto xg+(f)$ is $f$.

2 votes
3 answers
87 views

Number of elements $a\in\mathbb{F}_{5^4}$ such that $\mathbb{F}_{5^4}=\mathbb{F}_5(a)$

2 votes
1 answer
81 views

$K$-invariant $F$-homomorphism over finite normal field extension $K/F$

2 votes
1 answer
127 views

Find a Galois extension $\mathbb{Q}\subset K$ with $\text{Gal}(K/\mathbb{Q})\cong\mathbb{Z}/3\mathbb{Z}\times\mathbb{Z}/3\mathbb{Z}$

2 votes
1 answer
80 views

Show $(29,x^2+1)\subset\mathbb{Z}[x]$ is not a maximal ideal

2 votes
1 answer
68 views

Direct sum of subspaces using Cayley-Hamilton

2 votes
2 answers
110 views

Show set of matrices forms a finite field of order 27

2 votes
1 answer
45 views

How many elements of order $p^7$ are in $C_{p^5}\times C_{p^6}\times C_{p^7} \times C_{p^8}\times C_{p^9}$?