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user108580
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5 votes
1 answer
196 views

When is general linear group isomorphic to special linear group?

4 votes
1 answer
125 views

Prove that $\operatorname{GL}_n(k)$ and $\operatorname{SL}_n(k)$ cannot be symmetric group?

3 votes
0 answers
106 views

Prove there is a unique non-abelian group of order 75.

2 votes
0 answers
51 views

Find all units in the ring $\Bbb Z[\omega]$ where $\omega$ is the primitive $p^{th}$ root of unity.

2 votes
1 answer
94 views

$1\otimes_A x = 0$ in $A\otimes_A M$ then $x=0$.

2 votes
0 answers
59 views

Arc length of $(y-\sqrt[3]{x^2})^2+x^2 = 1$.

2 votes
0 answers
49 views

Prove $\left[F:\operatorname{Fix}(G)\right] \geq |G|$ if $G$ is finite and acts faithfully on $F$.

2 votes
2 answers
142 views

Find the sum of cube root of the roots of a cubic equation.

2 votes
0 answers
86 views

Solve $\frac{dy}{dx}=\frac{2x^2-xy+y^2}{y-x}$.

2 votes
0 answers
39 views

What would fail if "second countable" is replaced by "paracompact" in the definition of manifold?

1 vote
0 answers
50 views

Automorphism group gives the Galois group over the fixed field.

1 vote
0 answers
32 views

Why generalized eigenvectors give the Jordan normal form.

1 vote
1 answer
40 views

Galois Theory and the Rational Functions Field.

1 vote
1 answer
109 views

Prove that the map $z\mapsto \frac 1 2\left(z+\frac 1 z\right)$ is a homeomorphism.

1 vote
0 answers
68 views

What is the Correct Definition of Eigenvalue?

1 vote
1 answer
31 views

Why Smith normal form gives isomorphic modules?

1 vote
0 answers
95 views

Find a cubic polynomial with given property.

1 vote
0 answers
109 views

A proof of a special case of Dirichlet's theorem. [duplicate]

1 vote
0 answers
127 views

Prove that $x$ is irreducible in $\Bbb C[x,y]/(x^3+y^3-1)$

1 vote
0 answers
45 views

Determine if $(x^5+x^3y^2+x^2y^3+y^5-y)$ is a prime ideal in $\Bbb Q[x,y]$.

1 vote
1 answer
92 views

Definition of limits of a function in general.

1 vote
1 answer
76 views

The notion of "units" is independent of the base algebraic integer ring. [duplicate]

1 vote
1 answer
67 views

Conjugate images induce isomorphic semi-direct products?

0 votes
0 answers
50 views

Classify groups of order 20. [duplicate]

0 votes
0 answers
37 views

Existence of complex-valued limits.

0 votes
1 answer
133 views

Factor $x^5+x^4+x^3+x^2+x+1$ over $\Bbb F_5$

0 votes
0 answers
54 views

Compute normalizer of $\left<s,r^4\right>$ in $D_{16}$

0 votes
0 answers
42 views

Deduce Jordan Normal Form from PID finitely generated module structure.

0 votes
1 answer
40 views

Extension Property does not imply Normality.

0 votes
0 answers
57 views

If $\sqrt{n}$ is contained in $\Bbb Q[\omega_m]$, so does $\sqrt{p}$ for any $p|n$.