Question

Infinite integral domain may not be a field

score 1.1k · Answer 1 · 2026-04-12 01:46:50

1.1k

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Infinite integral domain may not be a field

Published on 12 Apr 2026 - 1:46

score 167 · Answer 2 · 2026-04-13 01:29:38

167

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Let $K$ be a subfield of $\mathbb{C}$ and let $f$ be an irreducible polynomial in $K$. Prove $f$ has no repeated roots in $\mathbb{C}$

Published on 13 Apr 2026 - 1:29

score 621 · Answer 3 · 2026-05-10 14:25:51

621

Views

Any $R$-module is a quotient of some free module. Do we need "finitely generated" condition?

Published on 10 May 2026 - 14:25

score 112 · Answer 4 · 2026-04-16 03:46:27

112

Views

Using Result of Nontrivial Center show that Every prime power order group contain subgroups of all prime power order

Published on 16 Apr 2026 - 3:46

score 44 · Answer 5 · 2026-04-10 05:08:46

44

Views

Extensions field in Galois Theory. Check Proof.

Published on 10 Apr 2026 - 5:08

score 331 · Answer 6 · 2026-05-10 17:48:40

331

Views

The induced representation of a trivial representation

Published on 10 May 2026 - 17:48

score 639 · Answer 7 · 2026-04-13 20:30:02

639

Views

Lorenzini's "Invitation to arithmetic geometry", 1st exercise

Published on 13 Apr 2026 - 20:30

score 4k · Answer 8 · 2026-04-12 03:55:56

4k

Views

order of elements in $\mathbb{Z}_p^*$ with $p$ prime

Published on 12 Apr 2026 - 3:55

score 801 · Answer 9 · 2026-04-08 23:13:06

801

Views

How do you interpret a product of transpositions?

Published on 08 Apr 2026 - 23:13

score 59 · Answer 10 · 2026-04-13 18:00:54

59

Views

On the cardinality of some quotient rings

Published on 13 Apr 2026 - 18:00

score 452 · Answer 11 · 2026-05-07 18:04:21

452

Views

Reference on correspondence between commutative Hopf Algebras and Groups

Published on 07 May 2026 - 18:04

score 531 · Answer 12 · 2026-04-16 03:00:19

531

Views

Let $\sigma \in\operatorname{Aut}(K)$ have infinite order and $F = \mathcal{F}(\sigma)$. Show that if $K/F$ is algebraic, then $K$ is normal over $F$.

Published on 16 Apr 2026 - 3:00

score 173 · Answer 13 · 2026-04-15 08:50:15

173

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Proving $\text{Gal}(K/F) \cong \text{Gal}(K/E_1) \times \text{Gal}(K/E_2)$

Published on 15 Apr 2026 - 8:50

score 28 · Answer 14 · 2026-04-14 08:56:25

28

Views

Intersection of an ideal with a subset

Published on 14 Apr 2026 - 8:56

score 110 · Answer 15 · 2026-05-10 12:39:06

110

Views

If $\left(E, \cdot\right)$ is a commutative semigroup of idempotents, then $\left(E,\leq\right)$ is an upper semilattice.

Published on 10 May 2026 - 12:39

List Question

Infinite integral domain may not be a field

Let $K$ be a subfield of $\mathbb{C}$ and let $f$ be an irreducible polynomial in $K$. Prove $f$ has no repeated roots in $\mathbb{C}$

Any $R$-module is a quotient of some free module. Do we need "finitely generated" condition?

Using Result of Nontrivial Center show that Every prime power order group contain subgroups of all prime power order

Extensions field in Galois Theory. Check Proof.

The induced representation of a trivial representation

Lorenzini's "Invitation to arithmetic geometry", 1st exercise

order of elements in $\mathbb{Z}_p^*$ with $p$ prime

How do you interpret a product of transpositions?

On the cardinality of some quotient rings

Reference on correspondence between commutative Hopf Algebras and Groups

Let $\sigma \in\operatorname{Aut}(K)$ have infinite order and $F = \mathcal{F}(\sigma)$. Show that if $K/F$ is algebraic, then $K$ is normal over $F$.

Proving $\text{Gal}(K/F) \cong \text{Gal}(K/E_1) \times \text{Gal}(K/E_2)$

Intersection of an ideal with a subset

If $\left(E, \cdot\right)$ is a commutative semigroup of idempotents, then $\left(E,\leq\right)$ is an upper semilattice.

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