Question

Prove that the irreducible polynomial for $\sqrt2+\sqrt3$ over $\mathbb{Q}$ is reducible modulo $p$ for every prime $p$

score 502 · Answer 1 · 2026-05-11 10:11:05

502

Views

Prove that the irreducible polynomial for $\sqrt2+\sqrt3$ over $\mathbb{Q}$ is reducible modulo $p$ for every prime $p$

Published on 11 May 2026 - 10:11

score 410 · Answer 2 · 2026-04-15 15:32:36

410

Views

What is the Galois Group of $f(t)=t^6-2t^3-1$ over $K:=\mathbb{Q}$?

Published on 15 Apr 2026 - 15:32

score 1.1k · Answer 3 · 2026-04-13 09:32:24

1.1k

Views

an odd degree polynomial with cyclic Galois group has root all real

Published on 13 Apr 2026 - 9:32

score 150 · Answer 4 · 2026-05-10 12:35:32

150

Views

$A = \langle p \rangle$ is a prime ideal of $\mathbb{Z}_n$ if and only if $p$ is a prime divisor of $n$

Published on 10 May 2026 - 12:35

score 798 · Answer 5 · 2026-05-11 10:00:01

798

Views

Understanding Kronecker's Theorem

Published on 11 May 2026 - 10:00

score 659 · Answer 6 · 2026-05-10 12:34:29

659

Views

Show that if $R$ is an integral domain, then $R[x]$ is an integral domain

Published on 10 May 2026 - 12:34

score 128 · Answer 7 · 2026-04-15 19:56:01

128

Views

Theorem 8.4 in Matsumura's Commutative Algebra

Published on 15 Apr 2026 - 19:56

score 508 · Answer 8 · 2026-04-15 12:28:56

508

Views

Prove that a polynomial ring over R in inﬁnitely many variables is non-Noetherian.

Published on 15 Apr 2026 - 12:28

score 82 · Answer 9 · 2026-05-13 04:57:16

82

Views

question about one possible way of constructing Grothendieck group

Published on 13 May 2026 - 4:57

score 128 · Answer 10 · 2026-04-14 05:20:04

128

Views

Prove $\operatorname{Gal}(L/K)$ is Abelian

Published on 14 Apr 2026 - 5:20

score 101 · Answer 11 · 2026-04-14 19:33:35

101

Views

Finding $(x-1)^{-2}$ in Quotient Ring

Published on 14 Apr 2026 - 19:33

score 1k · Answer 12 · 2026-04-14 03:07:07

1k

Views

What is the difference between $\Bbb F_4$ and $\Bbb Z/4\Bbb Z$

Published on 14 Apr 2026 - 3:07

score 347 · Answer 13 · 2026-05-11 10:11:38

347

Views

Prove that a polynomial of the form $x^p−x−a \in F[x]$ is either irreducible or splits in $F$.

Published on 11 May 2026 - 10:11

score 147 · Answer 14 · 2026-04-14 06:47:41

147

Views

For which fields $F$ and primes $p$ does the polynomial $x^p-x\in F[x]$ have a “multiple” root

Published on 14 Apr 2026 - 6:47

score 47 · Answer 15 · 2026-04-14 16:20:42

47

Views

Prove that $F(x, y)$ is a simple extension over $F(x^2 , y^2)$

Published on 14 Apr 2026 - 16:20

List Question

Prove that the irreducible polynomial for $\sqrt2+\sqrt3$ over $\mathbb{Q}$ is reducible modulo $p$ for every prime $p$

What is the Galois Group of $f(t)=t^6-2t^3-1$ over $K:=\mathbb{Q}$?

an odd degree polynomial with cyclic Galois group has root all real

$A = \langle p \rangle$ is a prime ideal of $\mathbb{Z}_n$ if and only if $p$ is a prime divisor of $n$

Understanding Kronecker's Theorem

Show that if $R$ is an integral domain, then $R[x]$ is an integral domain

Theorem 8.4 in Matsumura's Commutative Algebra

Prove that a polynomial ring over R in inﬁnitely many variables is non-Noetherian.

question about one possible way of constructing Grothendieck group

Prove $\operatorname{Gal}(L/K)$ is Abelian

Finding $(x-1)^{-2}$ in Quotient Ring

What is the difference between $\Bbb F_4$ and $\Bbb Z/4\Bbb Z$

Prove that a polynomial of the form $x^p−x−a \in F[x]$ is either irreducible or splits in $F$.

For which fields $F$ and primes $p$ does the polynomial $x^p-x\in F[x]$ have a “multiple” root

Prove that $F(x, y)$ is a simple extension over $F(x^2 , y^2)$

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