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MooS
  • Member for 7 years, 5 months
  • Last seen more than 2 years ago
26 votes
Accepted

how to prove an element is non-zero in a tensor-product

22 votes

Prove that $f=(x+i)^{10}+(x-i)^{10}$ have all real roots

19 votes
Accepted

Nilpotent matrix and relation between its powers and dimension of kernels

17 votes
Accepted

General linear group is an affine variety

17 votes

Show that $\langle 13 \rangle$ is a prime ideal in $\mathbb{Z[\sqrt{-5}]}$

15 votes
Accepted

Number of subgroups of an infinite group

14 votes

Irreducible polynomial over $\mathbb{Q}$ implies polynomial is irreducible over $\mathbb{Z}$

14 votes
Accepted

$R/Ra$ is an injective module over itself

13 votes
Accepted

Galois group of an irreducible , separable polynomial be abelian , then each of the roots of the polynomial generates the splitting field?

13 votes

A finite field extension of $\mathbb R$ is either $\mathbb R$ or isomorphic to $\mathbb C$

12 votes
Accepted

One-dimensional [Noetherian] UFD is a PID

12 votes
Accepted

Functional equation $x\space f(x^2) = f(x)$

10 votes
Accepted

A matrix is the unit matrix iff any equation of the form $X^{k}=A$ has at least one solution.

10 votes
Accepted

Maximize the value of $v^{T}Av$

10 votes

If a polynomial takes integer values at every integer, does it have integer coefficients?

10 votes
Accepted

Prove that $\sin x<x$, if $x>0$

10 votes
Accepted

If $A$ and $B$ are normal such that $AB=0$, does it follows that $BA=0$?

10 votes
Accepted

To prove f'(0)=f''(0)=0. Given F is twice differential

9 votes
Accepted

Auslander-Buchsbaum formula - proof

9 votes
Accepted

Is a Hamel basis dense?

9 votes

I have this conjecture. can you please give me a proof? I could not find proof.

9 votes
Accepted

Inverse of matrix whose row sums is 1

9 votes
Accepted

Basis for Tensor Product of Infinite Dimensional Vector Spaces

9 votes
Accepted

Show that $V(y^5-x^2)\subset \mathbb{R}^2$ is not isomorphic to $\mathbb{R}$ as a variety.

9 votes
Accepted

Pythagorean Triples : Is every positive integer $\gt$ $2$ part of at least one Pythagorean triple?

9 votes
Accepted

Bijection between $\mathbb{Z} \longmapsto \mathbb{R}$

9 votes

$x^p -x-c$ is irreducible over a field of characteristic $p$ if it has no root in the field

8 votes
Accepted

Geometric interpretation of primitive element theorem?

8 votes
Accepted

Show $\text{det}(A)$ is divisible by $2^{n-1}$

8 votes
Accepted

Question about field extension

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