Question

$K_1 K_2$ is equal to $F(a_1,... ,a_n,b_1,... ,b_m)$.

score 34 · Answer 1 · 2026-04-15 14:14:25

34

Views

$K_1 K_2$ is equal to $F(a_1,... ,a_n,b_1,... ,b_m)$.

Published on 15 Apr 2026 - 14:14

score 166 · Answer 2 · 2026-04-16 13:58:23

166

Views

Field of order $4$,$\{0,1,a,b\}$

Published on 16 Apr 2026 - 13:58

score 49 · Answer 3 · 2026-04-13 04:29:48

49

Views

Resultants and algebraic numbers

Published on 13 Apr 2026 - 4:29

score 273 · Answer 4 · 2026-04-15 03:02:40

273

Views

$(\mathbb R, \oplus)$ is a group. Define a multiplication with which we get a field. Where $a \oplus b = a + b +1$

Published on 15 Apr 2026 - 3:02

score 98 · Answer 5 · 2026-03-26 03:10:34

98

Views

$B$ spans algebraically $E$ over $F$

Published on 26 Mar 2026 - 3:10

score 53 · Answer 6 · 2026-04-16 14:49:07

53

Views

Given a field, $K$, are there two DVRs $A,B$ for the same field $K$, such that $A\cap B$ is also a field?

Published on 16 Apr 2026 - 14:49

score 185 · Answer 7 · 2026-04-15 11:45:30

185

Views

Given a complete discrete valuation field $L$, is there always a complete local field $K\subset L$?

Published on 15 Apr 2026 - 11:45

score 234 · Answer 8 · 2026-04-14 04:35:41

234

Views

Field with 2 elements

Published on 14 Apr 2026 - 4:35

score 119 · Answer 9 · 2026-04-16 09:53:06

119

Views

Find a primitive element for the extension $\mathbb Q(i,\sqrt3,e^{{\pi i/4}})/\mathbb Q$.

Published on 16 Apr 2026 - 9:53

score 1.9k · Answer 10 · 2026-04-17 08:37:45

1.9k

Views

If every element of R has a (multiplicative) inverse, then $R = \{0\}$

Published on 17 Apr 2026 - 8:37

score 40 · Answer 11 · 2026-04-16 05:33:43

40

Views

Assume $f(x)=(1+x)^n\in \mathbb F_p[x]$, can we find a general formula for $f(x)$?

Published on 16 Apr 2026 - 5:33

score 94 · Answer 12 · 2026-04-13 17:37:18

94

Views

what is the relation between of minimal polynomials of elements of two isomorphic fields?

Published on 13 Apr 2026 - 17:37

score 5.7k · Answer 13 · 2026-04-14 09:02:44

5.7k

Views

Finding a Galois extension of $\Bbb Q$ of degree $3$

Published on 14 Apr 2026 - 9:02

score 160 · Answer 14 · 2026-04-16 23:07:49

160

Views

$\mathbb F_4 \otimes_{\mathbb F_2}\mathbb F_8$ is isomorphic to $\mathbb F_{64}.$

Published on 16 Apr 2026 - 23:07

score 2k · Answer 15 · 2026-04-13 21:48:29

2k

Views

Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal

Published on 13 Apr 2026 - 21:48

List Question

$K_1 K_2$ is equal to $F(a_1,... ,a_n,b_1,... ,b_m)$.

Field of order $4$,$\{0,1,a,b\}$

Resultants and algebraic numbers

$(\mathbb R, \oplus)$ is a group. Define a multiplication with which we get a field. Where $a \oplus b = a + b +1$

$B$ spans algebraically $E$ over $F$

Given a field, $K$, are there two DVRs $A,B$ for the same field $K$, such that $A\cap B$ is also a field?

Given a complete discrete valuation field $L$, is there always a complete local field $K\subset L$?

Field with 2 elements

Find a primitive element for the extension $\mathbb Q(i,\sqrt3,e^{{\pi i/4}})/\mathbb Q$.

If every element of R has a (multiplicative) inverse, then $R = \{0\}$

Assume $f(x)=(1+x)^n\in \mathbb F_p[x]$, can we find a general formula for $f(x)$?

what is the relation between of minimal polynomials of elements of two isomorphic fields?

Finding a Galois extension of $\Bbb Q$ of degree $3$

$\mathbb F_4 \otimes_{\mathbb F_2}\mathbb F_8$ is isomorphic to $\mathbb F_{64}.$

Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal

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