Question regarding Galois theory
$begingroup$
While reading a theorem on Galois theory I came up with this statement "Let $E/F$ be a finite separable extension. Then $E$ is contained in an extension of $K$ which is Galois over $F$.
Now my question is about first statement. Because according as what I know if$E/F$ is a finite extension then it's an algebraic extension and as it's separable hence it's a normal extension also. So $E/F$ is normal separable extension, hence it is Galois. So what am I thinking wrong. It will be really great if you can help me with it
galois-theory galois-extensions
edited Jan 4 at 17:45
Bernard
120k740113
asked Jan 4 at 16:46
user631697user631697
111
$endgroup$
|
show 1 more comment
$begingroup$
While reading a theorem on Galois theory I came up with this statement "Let $E/F$ be a finite separable extension. Then $E$ is contained in an extension of $K$ which is Galois over $F$.
Now my question is about first statement. Because according as what I know if$E/F$ is a finite extension then it's an algebraic extension and as it's separable hence it's a normal extension also. So $E/F$ is normal separable extension, hence it is Galois. So what am I thinking wrong. It will be really great if you can help me with it
galois-theory galois-extensions
edited Jan 4 at 17:45
Bernard
120k740113
asked Jan 4 at 16:46
user631697user631697
111
$endgroup$
$begingroup$
not every separable extension is normal.
$endgroup$
– Lord Shark the Unknown
Jan 4 at 17:02
$begingroup$
I know not every separable extension isn't normal. But isn't every separable finite extension normal. As even finite extension is algebric.
$endgroup$
– user631697
Jan 4 at 17:06
$begingroup$
not every separable finite extension is normal.
$endgroup$
– Lord Shark the Unknown
Jan 4 at 17:07
$begingroup$
It will be great if u can give an example
$endgroup$
– user631697
Jan 4 at 17:08
1
$begingroup$
$Bbb Q(sqrt[3]5,)supsetBbb Q$
$endgroup$
– Lubin
Jan 4 at 17:35
|
show 1 more comment
$begingroup$
While reading a theorem on Galois theory I came up with this statement "Let $E/F$ be a finite separable extension. Then $E$ is contained in an extension of $K$ which is Galois over $F$.
Now my question is about first statement. Because according as what I know if$E/F$ is a finite extension then it's an algebraic extension and as it's separable hence it's a normal extension also. So $E/F$ is normal separable extension, hence it is Galois. So what am I thinking wrong. It will be really great if you can help me with it
galois-theory galois-extensions
edited Jan 4 at 17:45
Bernard
120k740113
asked Jan 4 at 16:46
user631697user631697
111
$endgroup$
While reading a theorem on Galois theory I came up with this statement "Let $E/F$ be a finite separable extension. Then $E$ is contained in an extension of $K$ which is Galois over $F$.
Now my question is about first statement. Because according as what I know if$E/F$ is a finite extension then it's an algebraic extension and as it's separable hence it's a normal extension also. So $E/F$ is normal separable extension, hence it is Galois. So what am I thinking wrong. It will be really great if you can help me with it
galois-theory galois-extensions
galois-theory galois-extensions
edited Jan 4 at 17:45
Bernard
120k740113
asked Jan 4 at 16:46
user631697user631697
111
edited Jan 4 at 17:45
Bernard
120k740113
asked Jan 4 at 16:46
user631697user631697
111
edited Jan 4 at 17:45
Bernard
120k740113
edited Jan 4 at 17:45
Bernard
120k740113
edited Jan 4 at 17:45
Bernard
120k740113
120k740113
asked Jan 4 at 16:46
user631697user631697
111
asked Jan 4 at 16:46
user631697user631697
111
asked Jan 4 at 16:46
user631697user631697
111
111
$begingroup$
not every separable extension is normal.
$endgroup$
– Lord Shark the Unknown
Jan 4 at 17:02
$begingroup$
I know not every separable extension isn't normal. But isn't every separable finite extension normal. As even finite extension is algebric.
$endgroup$
– user631697
Jan 4 at 17:06
$begingroup$
not every separable finite extension is normal.
$endgroup$
– Lord Shark the Unknown
Jan 4 at 17:07
$begingroup$
It will be great if u can give an example
$endgroup$
– user631697
Jan 4 at 17:08
1
$begingroup$
$Bbb Q(sqrt[3]5,)supsetBbb Q$
$endgroup$
– Lubin
Jan 4 at 17:35
|
show 1 more comment
$begingroup$
not every separable extension is normal.
$endgroup$
– Lord Shark the Unknown
Jan 4 at 17:02
$begingroup$
I know not every separable extension isn't normal. But isn't every separable finite extension normal. As even finite extension is algebric.
$endgroup$
– user631697
Jan 4 at 17:06
$begingroup$
not every separable finite extension is normal.
$endgroup$
– Lord Shark the Unknown
Jan 4 at 17:07
$begingroup$
It will be great if u can give an example
$endgroup$
– user631697
Jan 4 at 17:08
1
$begingroup$
$Bbb Q(sqrt[3]5,)supsetBbb Q$
$endgroup$
– Lubin
Jan 4 at 17:35
$begingroup$
not every separable extension is normal.
$endgroup$
– Lord Shark the Unknown
Jan 4 at 17:02
$begingroup$
not every separable extension is normal.
$endgroup$
– Lord Shark the Unknown
Jan 4 at 17:02
$begingroup$
I know not every separable extension isn't normal. But isn't every separable finite extension normal. As even finite extension is algebric.
$endgroup$
– user631697
Jan 4 at 17:06
$begingroup$
I know not every separable extension isn't normal. But isn't every separable finite extension normal. As even finite extension is algebric.
$endgroup$
– user631697
Jan 4 at 17:06
$begingroup$
not every separable finite extension is normal.
$endgroup$
– Lord Shark the Unknown
Jan 4 at 17:07
$begingroup$
not every separable finite extension is normal.
$endgroup$
– Lord Shark the Unknown
Jan 4 at 17:07
$begingroup$
It will be great if u can give an example
$endgroup$
– user631697
Jan 4 at 17:08
$begingroup$
It will be great if u can give an example
$endgroup$
– user631697
Jan 4 at 17:08
1
1
$begingroup$
$Bbb Q(sqrt[3]5,)supsetBbb Q$
$endgroup$
– Lubin
Jan 4 at 17:35
$begingroup$
$Bbb Q(sqrt[3]5,)supsetBbb Q$
$endgroup$
– Lubin
Jan 4 at 17:35
|
show 1 more comment
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$begingroup$
not every separable extension is normal.
$endgroup$
– Lord Shark the Unknown
Jan 4 at 17:02
$begingroup$
I know not every separable extension isn't normal. But isn't every separable finite extension normal. As even finite extension is algebric.
$endgroup$
– user631697
Jan 4 at 17:06
$begingroup$
not every separable finite extension is normal.
$endgroup$
– Lord Shark the Unknown
Jan 4 at 17:07
$begingroup$
It will be great if u can give an example
$endgroup$
– user631697
Jan 4 at 17:08
1
$begingroup$
$Bbb Q(sqrt[3]5,)supsetBbb Q$
$endgroup$
– Lubin
Jan 4 at 17:35