Which theorem tells about smallest field containing two given fields?
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Suppose $mathbb{F} _{p^n}$ and $mathbb{F} _{p^m}$ are two finite fields where p is a prime number and n,m$in mathbb{N}$, what is the smallest field containing these fields ?
field-theory splitting-field
asked Nov 13 at 22:59
Vinay Sipani
515
add a comment |
up vote
0
down vote
favorite
Suppose $mathbb{F} _{p^n}$ and $mathbb{F} _{p^m}$ are two finite fields where p is a prime number and n,m$in mathbb{N}$, what is the smallest field containing these fields ?
field-theory splitting-field
asked Nov 13 at 22:59
Vinay Sipani
515
Look up compositum.
– user10354138
Nov 14 at 0:47
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Suppose $mathbb{F} _{p^n}$ and $mathbb{F} _{p^m}$ are two finite fields where p is a prime number and n,m$in mathbb{N}$, what is the smallest field containing these fields ?
field-theory splitting-field
asked Nov 13 at 22:59
Vinay Sipani
515
Suppose $mathbb{F} _{p^n}$ and $mathbb{F} _{p^m}$ are two finite fields where p is a prime number and n,m$in mathbb{N}$, what is the smallest field containing these fields ?
field-theory splitting-field
field-theory splitting-field
asked Nov 13 at 22:59
Vinay Sipani
515
asked Nov 13 at 22:59
Vinay Sipani
515
asked Nov 13 at 22:59
Vinay Sipani
515
asked Nov 13 at 22:59
Vinay Sipani
515
asked Nov 13 at 22:59
Vinay Sipani
515
515
Look up compositum.
– user10354138
Nov 14 at 0:47
add a comment |
Look up compositum.
– user10354138
Nov 14 at 0:47
Look up compositum.
– user10354138
Nov 14 at 0:47
Look up compositum.
– user10354138
Nov 14 at 0:47
add a comment |
1 Answer
1
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2
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$Bbb F_{p^k}subseteqBbb F_{p^h}$ if and only if $kmid h$. Therefore you are looking for $Bbb F_{p^{operatorname{lcm}(n,m)}}$.
answered Nov 13 at 23:05
Saucy O'Path
5,4671425
Where can I get a proof of this statement and also that explains about the subfields of a finite field ?
– Vinay Sipani
Nov 13 at 23:08
I guess your algebra textbook should have that proof. I don't know what you are referring to in the second question.
– Saucy O'Path
Nov 13 at 23:09
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
$Bbb F_{p^k}subseteqBbb F_{p^h}$ if and only if $kmid h$. Therefore you are looking for $Bbb F_{p^{operatorname{lcm}(n,m)}}$.
answered Nov 13 at 23:05
Saucy O'Path
5,4671425
Where can I get a proof of this statement and also that explains about the subfields of a finite field ?
– Vinay Sipani
Nov 13 at 23:08
I guess your algebra textbook should have that proof. I don't know what you are referring to in the second question.
– Saucy O'Path
Nov 13 at 23:09
add a comment |
up vote
2
down vote
$Bbb F_{p^k}subseteqBbb F_{p^h}$ if and only if $kmid h$. Therefore you are looking for $Bbb F_{p^{operatorname{lcm}(n,m)}}$.
answered Nov 13 at 23:05
Saucy O'Path
5,4671425
Where can I get a proof of this statement and also that explains about the subfields of a finite field ?
– Vinay Sipani
Nov 13 at 23:08
I guess your algebra textbook should have that proof. I don't know what you are referring to in the second question.
– Saucy O'Path
Nov 13 at 23:09
add a comment |
up vote
2
down vote
up vote
2
down vote
$Bbb F_{p^k}subseteqBbb F_{p^h}$ if and only if $kmid h$. Therefore you are looking for $Bbb F_{p^{operatorname{lcm}(n,m)}}$.
answered Nov 13 at 23:05
Saucy O'Path
5,4671425
$Bbb F_{p^k}subseteqBbb F_{p^h}$ if and only if $kmid h$. Therefore you are looking for $Bbb F_{p^{operatorname{lcm}(n,m)}}$.
answered Nov 13 at 23:05
Saucy O'Path
5,4671425
answered Nov 13 at 23:05
Saucy O'Path
5,4671425
answered Nov 13 at 23:05
Saucy O'Path
5,4671425
answered Nov 13 at 23:05
Saucy O'Path
5,4671425
5,4671425
Where can I get a proof of this statement and also that explains about the subfields of a finite field ?
– Vinay Sipani
Nov 13 at 23:08
I guess your algebra textbook should have that proof. I don't know what you are referring to in the second question.
– Saucy O'Path
Nov 13 at 23:09
add a comment |
Where can I get a proof of this statement and also that explains about the subfields of a finite field ?
– Vinay Sipani
Nov 13 at 23:08
I guess your algebra textbook should have that proof. I don't know what you are referring to in the second question.
– Saucy O'Path
Nov 13 at 23:09
Where can I get a proof of this statement and also that explains about the subfields of a finite field ?
– Vinay Sipani
Nov 13 at 23:08
Where can I get a proof of this statement and also that explains about the subfields of a finite field ?
– Vinay Sipani
Nov 13 at 23:08
I guess your algebra textbook should have that proof. I don't know what you are referring to in the second question.
– Saucy O'Path
Nov 13 at 23:09
I guess your algebra textbook should have that proof. I don't know what you are referring to in the second question.
– Saucy O'Path
Nov 13 at 23:09
add a comment |
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Look up compositum.
– user10354138
Nov 14 at 0:47