User Auclair

5 votes

1 answer

493 views

Hausdorff spaces and separated maps.

general-topology

asked May 20, 2016 at 12:28

4 votes

1 answer

874 views

Puzzle about sorting coins while blindfolded

combinatorics puzzle

asked Dec 15, 2015 at 18:02

4 votes

1 answer

230 views

I'm going to do a project on braid groups, and I'm looking for recommendations on books about braid groups.

abstract-algebra braid-groups

asked Mar 16, 2016 at 0:18

3 votes

2 answers

70 views

If $H \triangleleft K \leqslant G$, which requirements must be placed on $K$ in order to obtain $N \triangleleft G$?

abstract-algebra group-theory

asked Feb 8, 2016 at 11:14

3 votes

2 answers

68 views

Is there a "clever" way to solve this congruence?

number-theory

asked Dec 4, 2015 at 10:20

3 votes

2 answers

576 views

Is this ring R both noetherian and artinian?

abstract-algebra ring-theory noetherian

asked Dec 9, 2015 at 13:04

3 votes

2 answers

96 views

Explicit automorphisms of the splitting field of a certain quartic over the rationals.

field-theory finite-groups galois-theory extension-field abelian-groups

asked May 30, 2016 at 20:43

3 votes

1 answer

65 views

Is this enough to justify an internal direct product?

abstract-algebra group-theory finite-groups

asked Mar 13, 2016 at 19:08

3 votes

0 answers

91 views

Why are the morphisms in an Auslander-Reiten triangle irreducible?

abstract-algebra category-theory representation-theory triangulated-categories

asked Dec 10, 2018 at 13:22

3 votes

1 answer

159 views

Understanding the morphism category (arrow category)

abstract-algebra category-theory homological-algebra

asked Mar 22, 2019 at 14:35

3 votes

1 answer

59 views

Trying to understand some formulas about dualities, specifically $\operatorname{Hom}_{\Lambda}(Y,\nu X) \cong D\operatorname{Hom}_{\Lambda}(X,Y)$.

abstract-algebra representation-theory dual-spaces

asked May 21, 2019 at 14:59

2 votes

1 answer

155 views

Minimal projective presentations from projective presentations.

abstract-algebra representation-theory

asked Apr 23, 2019 at 14:55

2 votes

2 answers

98 views

Two definitions of torsion pairs/theories. How are they equivalent?

abstract-algebra modules representation-theory

asked May 15, 2019 at 22:16

2 votes

1 answer

75 views

Are $1$-tilting modules always faithful?

abstract-algebra representation-theory

asked Apr 8, 2019 at 11:39

2 votes

0 answers

50 views

What does the weights of $\mathfrak{gl}(V)$ look like as a Lie-module?

lie-groups lie-algebras

asked Mar 6, 2018 at 0:22

2 votes

0 answers

63 views

Is this a bijection between $\mathcal{P}(\mathbb{R})$ and $\mathbb{R}^\mathbb{R}$

elementary-set-theory proof-verification

asked May 7, 2018 at 6:20

2 votes

0 answers

49 views

Help with notation/concepts in module theory and category theory, specifically $\operatorname{Add}(M)$, $\operatorname{Gen}(M)$ and $^\circ(M^\circ)$

category-theory modules

asked Aug 27, 2018 at 8:44

2 votes

2 answers

527 views

How do I show this isomorphism between an opposite endomorphism ring and a module over path algebras?

abstract-algebra ring-theory quiver

asked May 20, 2017 at 13:47

2 votes

1 answer

29 views

Order of $z\in Z(W)\backslash \{\rm{id}\}$ for $W$ the Weyl group.

lie-algebras root-systems

asked Feb 7, 2018 at 8:20

2 votes

2 answers

271 views

Given the splitting field of a polynomial, how can I show that there are three intermediate extensions which aren't normal?

field-theory galois-theory extension-field

asked May 29, 2016 at 14:30

2 votes

1 answer

215 views

I want to show how many intermediate fields there are between $GF(3^{12})$ and $GF(3^4)$.

field-theory galois-theory finite-fields extension-field

asked May 30, 2016 at 12:41

2 votes

4 answers

488 views

Prove $2^{1/2}+3^{1/3}$ is irrational using Galois theory.

field-theory galois-theory extension-field irrational-numbers

asked Jun 7, 2016 at 13:51

2 votes

1 answer

424 views

Density in a topological space.

general-topology

asked May 24, 2016 at 10:20

2 votes

1 answer

835 views

What is the Galois group $Gal(E/F)$ when $F=GF(5^3)$ and $E=GF(5^{24})$

galois-theory finite-fields

asked May 25, 2016 at 10:59

2 votes

1 answer

2k views

Is the surface of a torus 2-dimensional?

general-topology geometry

asked Apr 26, 2016 at 21:26

2 votes

1 answer

69 views

Is this an open covering of $X$ which has no finite subcover?

general-topology

asked May 13, 2016 at 9:38

2 votes

2 answers

1k views

Solving a cubic congruence equation with Chinese Remainder Theorem

number-theory elementary-number-theory modular-arithmetic cryptography chinese-remainder-theorem

asked Oct 6, 2015 at 11:18

2 votes

0 answers

282 views

A continuous bijection between finite topological spaces which is not a homeomorphism

general-topology

asked Apr 20, 2016 at 11:31

2 votes

2 answers

2k views

Irreducible polynomials over $GF(4)$.

galois-theory finite-fields

asked Apr 26, 2016 at 12:26

1 vote

1 answer

160 views

Find $\theta \neq \sqrt{3}+\sqrt{5}$ such that $\mathbb{Q}(\theta) = \mathbb{Q}(\sqrt{3},\sqrt{5})$. Need a hint to get started.

field-theory galois-theory extension-field

asked Apr 26, 2016 at 15:19

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92 Questions

Hausdorff spaces and separated maps.

Puzzle about sorting coins while blindfolded

I'm going to do a project on braid groups, and I'm looking for recommendations on books about braid groups.

If $H \triangleleft K \leqslant G$, which requirements must be placed on $K$ in order to obtain $N \triangleleft G$?

Is there a "clever" way to solve this congruence?

Is this ring R both noetherian and artinian?

Explicit automorphisms of the splitting field of a certain quartic over the rationals.

Is this enough to justify an internal direct product?

Why are the morphisms in an Auslander-Reiten triangle irreducible?

Understanding the morphism category (arrow category)

Trying to understand some formulas about dualities, specifically $\operatorname{Hom}_{\Lambda}(Y,\nu X) \cong D\operatorname{Hom}_{\Lambda}(X,Y)$.

Minimal projective presentations from projective presentations.

Two definitions of torsion pairs/theories. How are they equivalent?

Are $1$-tilting modules always faithful?

What does the weights of $\mathfrak{gl}(V)$ look like as a Lie-module?

Is this a bijection between $\mathcal{P}(\mathbb{R})$ and $\mathbb{R}^\mathbb{R}$

Help with notation/concepts in module theory and category theory, specifically $\operatorname{Add}(M)$, $\operatorname{Gen}(M)$ and $^\circ(M^\circ)$

How do I show this isomorphism between an opposite endomorphism ring and a module over path algebras?

Order of $z\in Z(W)\backslash \{\rm{id}\}$ for $W$ the Weyl group.

Given the splitting field of a polynomial, how can I show that there are three intermediate extensions which aren't normal?

I want to show how many intermediate fields there are between $GF(3^{12})$ and $GF(3^4)$.

Prove $2^{1/2}+3^{1/3}$ is irrational using Galois theory.

Density in a topological space.

What is the Galois group $Gal(E/F)$ when $F=GF(5^3)$ and $E=GF(5^{24})$

Is the surface of a torus 2-dimensional?

Is this an open covering of $X$ which has no finite subcover?

Solving a cubic congruence equation with Chinese Remainder Theorem

A continuous bijection between finite topological spaces which is not a homeomorphism

Irreducible polynomials over $GF(4)$.

Find $\theta \neq \sqrt{3}+\sqrt{5}$ such that $\mathbb{Q}(\theta) = \mathbb{Q}(\sqrt{3},\sqrt{5})$. Need a hint to get started.