Question

Understanding valutation and residue field

score 290 · Answer 1 · 2019-04-03 16:46:42

Understanding valutation and residue field

Published on 03 Apr 2019 - 16:46

score 140 · Answer 2 · 2026-03-31 11:09:46

With $[K: F] = 3, \alpha \in K, \beta \in K \backslash F$, show that there are $a,b,c,d \in F$ such that $\alpha = \frac{a+b\beta}{c+d\beta}$

score 139 · Answer 3 · 2026-03-27 03:42:19

139

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Trouble understanding converse of Tarski's theorem

Published on 27 Mar 2026 - 3:42

score 37 · Answer 4 · 2026-03-31 21:11:42

37

Views

Sum and product of the roots of $f(x)\in k[x]$ lie in k, where $k$ field and $f(x)$ monic non irreducible over $k.$

Published on 31 Mar 2026 - 21:11

score 89 · Answer 5 · 2019-04-04 02:00:25

89

Views

Is this a valid Zorn's Lemma proof on the existence and uniqueness of algebraic closures?

Published on 04 Apr 2019 - 2:00

score 56 · Answer 6 · 2026-03-31 21:10:35

56

Views

Ortbit of $\pi$ under the action of $\operatorname{Aut} \mathbb C $

Published on 31 Mar 2026 - 21:10

score 1.4k · Answer 7 · 2026-03-27 00:04:46

1.4k

Views

Infinite Abelian subgroup of infinite non Abelian group example

Published on 27 Mar 2026 - 0:04

score 155 · Answer 8 · 2026-03-27 00:05:19

155

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Show that a polynomial is irreducible in $\mathbb { Z } [ i \sqrt { 5 } ]$ but not in $\mathbb { Q } [ i \sqrt { 5 } ]$

Published on 27 Mar 2026 - 0:05

score 418 · Answer 9 · 2026-03-27 00:02:39

418

Views

Irreducible Polynomials In $F_3$

Published on 27 Mar 2026 - 0:02

score 60 · Answer 10 · 2026-03-31 13:04:34

60

Views

A question about extension field

Published on 31 Mar 2026 - 13:04

score 38 · Answer 11 · 2026-03-25 23:10:38

38

Views

extending automorphisms in a tower of fields

Published on 25 Mar 2026 - 23:10

score 29 · Answer 12 · 2026-03-31 22:49:43

29

Views

Finite Extension has Finitely Many Automorphisms?

Published on 31 Mar 2026 - 22:49

score 157 · Answer 13 · 2026-03-30 22:51:29

157

Views

Show that if $F$ is a field, $f(x) \in F[x]$, then $f(x) * F[x]$ is an ideal in $F[x]$, and every ideal of $F[x]$ is of this form.

Published on 30 Mar 2026 - 22:51

score 199 · Answer 14 · 2026-03-28 17:40:28

199

Views

Is there a principal maximal ideal in $\mathbb F_q[X,Y]$?

Published on 28 Mar 2026 - 17:40

score 76 · Answer 15 · 2026-03-31 22:51:10

76

Views

Help proving an alternative version of Chinese Residue Theorem in the ring of polynomials.

Published on 31 Mar 2026 - 22:51

List Question

Understanding valutation and residue field

With $[K: F] = 3, \alpha \in K, \beta \in K \backslash F$, show that there are $a,b,c,d \in F$ such that $\alpha = \frac{a+b\beta}{c+d\beta}$

Trouble understanding converse of Tarski's theorem

Sum and product of the roots of $f(x)\in k[x]$ lie in k, where $k$ field and $f(x)$ monic non irreducible over $k.$

Is this a valid Zorn's Lemma proof on the existence and uniqueness of algebraic closures?

Ortbit of $\pi$ under the action of $\operatorname{Aut} \mathbb C $

Infinite Abelian subgroup of infinite non Abelian group example

Show that a polynomial is irreducible in $\mathbb { Z } [ i \sqrt { 5 } ]$ but not in $\mathbb { Q } [ i \sqrt { 5 } ]$

Irreducible Polynomials In $F_3$

A question about extension field

extending automorphisms in a tower of fields

Finite Extension has Finitely Many Automorphisms?

Show that if $F$ is a field, $f(x) \in F[x]$, then $f(x) * F[x]$ is an ideal in $F[x]$, and every ideal of $F[x]$ is of this form.

Is there a principal maximal ideal in $\mathbb F_q[X,Y]$?

Help proving an alternative version of Chinese Residue Theorem in the ring of polynomials.

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