Let $K$ be a field. Prove that every element in $K(x)backslash K$ is transcendental
0
$begingroup$
Let $K$ be a field. Prove that every element in $K(x)backslash K$ is transcendental
over $K$.
Is proof of the question above similar to that of the question below?
field-theory transcendental-numbers
asked Dec 10 '18 at 23:29
Leyla AlkanLeyla Alkan
1,5751724
$endgroup$
add a comment |
0
$begingroup$
Let $K$ be a field. Prove that every element in $K(x)backslash K$ is transcendental
over $K$.
Is proof of the question above similar to that of the question below?
field-theory transcendental-numbers
asked Dec 10 '18 at 23:29
Leyla AlkanLeyla Alkan
1,5751724
$endgroup$
$begingroup$
Yes - let $F=K(x)$ and let $u=x$. Then it follows from the theorem.
$endgroup$
– ODF
Dec 11 '18 at 0:12
add a comment |
0
0
0
$begingroup$
Let $K$ be a field. Prove that every element in $K(x)backslash K$ is transcendental
over $K$.
Is proof of the question above similar to that of the question below?
field-theory transcendental-numbers
asked Dec 10 '18 at 23:29
Leyla AlkanLeyla Alkan
1,5751724
$endgroup$
Let $K$ be a field. Prove that every element in $K(x)backslash K$ is transcendental
over $K$.
Is proof of the question above similar to that of the question below?
field-theory transcendental-numbers
field-theory transcendental-numbers
asked Dec 10 '18 at 23:29
Leyla AlkanLeyla Alkan
1,5751724
asked Dec 10 '18 at 23:29
Leyla AlkanLeyla Alkan
1,5751724
edited Dec 10 '18 at 23:36
Leyla Alkan
asked Dec 10 '18 at 23:29
Leyla AlkanLeyla Alkan
1,5751724
asked Dec 10 '18 at 23:29
Leyla AlkanLeyla Alkan
1,5751724
asked Dec 10 '18 at 23:29
Leyla AlkanLeyla Alkan
1,5751724
1,5751724
$begingroup$
Yes - let $F=K(x)$ and let $u=x$. Then it follows from the theorem.
$endgroup$
– ODF
Dec 11 '18 at 0:12
add a comment |
$begingroup$
Yes - let $F=K(x)$ and let $u=x$. Then it follows from the theorem.
$endgroup$
– ODF
Dec 11 '18 at 0:12
$begingroup$
Yes - let $F=K(x)$ and let $u=x$. Then it follows from the theorem.
$endgroup$
– ODF
Dec 11 '18 at 0:12
$begingroup$
Yes - let $F=K(x)$ and let $u=x$. Then it follows from the theorem.
$endgroup$
– ODF
Dec 11 '18 at 0:12
add a comment |
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$begingroup$
Yes - let $F=K(x)$ and let $u=x$. Then it follows from the theorem.
$endgroup$
– ODF
Dec 11 '18 at 0:12