Question

How do we know which field we get in $\mathbb{Q}[x]/(x^3-2)$?

score 52 · Answer 1 · 2019-09-25 02:38:17

52

Views

How do we know which field we get in $\mathbb{Q}[x]/(x^3-2)$?

Published on 25 Sep 2019 - 2:38

score 118 · Answer 2 · 2026-03-29 20:39:34

118

Views

For any prime number $p$ and $m \in \Bbb N$ there exists a field of cardinality $p^m.$

Published on 29 Mar 2026 - 20:39

score 136 · Answer 3 · 2026-03-26 03:11:20

136

Views

Finite dimensional splitting field is generated by finite number of polynomials

Published on 26 Mar 2026 - 3:11

score 36 · Answer 4 · 2019-09-26 20:47:52

36

Views

I had to show that a' + b' = a + b mod n, when a mod n = a' and b mod n = b'

Published on 26 Sep 2019 - 20:47

score 68 · Answer 5 · 2026-04-01 09:55:33

68

Views

$α$ root of $f$, $β$ root of $g$. Show $f$ irred. in $\mathbb{Q}(β)$ iff $g$ irred. in $\mathbb{Q}(α)$

Published on 01 Apr 2026 - 9:55

score 126 · Answer 6 · 2026-03-26 23:10:45

126

Views

Proof check that the composite of $\sigma K$ is precisely the galois closure $L$ of $K/F$.

Published on 26 Mar 2026 - 23:10

score 35 · Answer 7 · 2026-04-01 09:54:07

35

Views

Proof about square roots of rational numbers being rational/irrational

Published on 01 Apr 2026 - 9:54

score 1k · Answer 8 · 2019-09-29 16:28:30

1k

Views

Maximal ideals of polynomials in two variables

Published on 29 Sep 2019 - 16:28

score 276 · Answer 9 · 2026-03-27 23:31:58

276

Views

When does the set of diagonal matrices over a finite prime field ($GL(n, F)$) form a normal subgroup?

Published on 27 Mar 2026 - 23:31

score 73 · Answer 10 · 2019-09-30 04:16:52

73

Views

$L/K \cong K$, then is $K=L$?

Published on 30 Sep 2019 - 4:16

score 277 · Answer 11 · 2026-03-27 11:46:34

277

Views

Why is $0.1 =1$ in the $p$-adic numbers?

Published on 27 Mar 2026 - 11:46

score 45 · Answer 12 · 2026-04-02 14:45:12

45

Views

Why does $\chi (L,L) \subseteq \text{End}_{K} (L)$?

Published on 02 Apr 2026 - 14:45

score 194 · Answer 13 · 2026-03-25 19:05:28

194

Views

Tangent and cotangent spaces of varieties over a field

Published on 25 Mar 2026 - 19:05

score 64 · Answer 14 · 2026-02-23 04:58:23

64

Views

Irreducible polynomial of the form $x^4+ax^2+b \in K[x]$, where $K$ is a field with char$K \neq 2$, is separable?

Published on 23 Feb 2026 - 4:58

score 163 · Answer 15 · 2026-03-26 09:44:47

163

Views

Unique "splitting fields" for infinite polynomials

Published on 26 Mar 2026 - 9:44

List Question

How do we know which field we get in $\mathbb{Q}[x]/(x^3-2)$?

For any prime number $p$ and $m \in \Bbb N$ there exists a field of cardinality $p^m.$

Finite dimensional splitting field is generated by finite number of polynomials

I had to show that a' + b' = a + b mod n, when a mod n = a' and b mod n = b'

$α$ root of $f$, $β$ root of $g$. Show $f$ irred. in $\mathbb{Q}(β)$ iff $g$ irred. in $\mathbb{Q}(α)$

Proof check that the composite of $\sigma K$ is precisely the galois closure $L$ of $K/F$.

Proof about square roots of rational numbers being rational/irrational

Maximal ideals of polynomials in two variables

When does the set of diagonal matrices over a finite prime field ($GL(n, F)$) form a normal subgroup?

$L/K \cong K$, then is $K=L$?

Why is $0.1 =1$ in the $p$-adic numbers?

Why does $\chi (L,L) \subseteq \text{End}_{K} (L)$?

Tangent and cotangent spaces of varieties over a field

Irreducible polynomial of the form $x^4+ax^2+b \in K[x]$, where $K$ is a field with char$K \neq 2$, is separable?

Unique "splitting fields" for infinite polynomials

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