Elements over transcendental extension
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
Let $F$ a field and suppose that $E$ is a extension field of $F$. Now, take $alphain E$ trascendental over $F$. My question is about the form of the elements of $F(alpha)$. I think that $$F(alpha)=leftfracf(alpha)g(alpha):f,gin F[x]right$$.
Am I right?
abstract-algebra soft-question extension-field
asked Aug 7 at 17:05
Gödel
1,145319
add a comment |Â
up vote
0
down vote
favorite
Let $F$ a field and suppose that $E$ is a extension field of $F$. Now, take $alphain E$ trascendental over $F$. My question is about the form of the elements of $F(alpha)$. I think that $$F(alpha)=leftfracf(alpha)g(alpha):f,gin F[x]right$$.
Am I right?
abstract-algebra soft-question extension-field
asked Aug 7 at 17:05
Gödel
1,145319
I think you meant "transcendental over $F$". As to your collection, it isn't clear what you mean. If $f,gin F[x]$ then $lambda f, lambda g$ define the same element of $F(alpha)$. And if you allow multiple expressions for the same element then your collection defines $F(alpha)$ even if $alpha $ is algebraic.
– lulu
Aug 7 at 17:10
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $F$ a field and suppose that $E$ is a extension field of $F$. Now, take $alphain E$ trascendental over $F$. My question is about the form of the elements of $F(alpha)$. I think that $$F(alpha)=leftfracf(alpha)g(alpha):f,gin F[x]right$$.
Am I right?
abstract-algebra soft-question extension-field
asked Aug 7 at 17:05
Gödel
1,145319
Let $F$ a field and suppose that $E$ is a extension field of $F$. Now, take $alphain E$ trascendental over $F$. My question is about the form of the elements of $F(alpha)$. I think that $$F(alpha)=leftfracf(alpha)g(alpha):f,gin F[x]right$$.
Am I right?
abstract-algebra soft-question extension-field
asked Aug 7 at 17:05
Gödel
1,145319
edited Aug 7 at 17:12
asked Aug 7 at 17:05
Gödel
1,145319
asked Aug 7 at 17:05
Gödel
1,145319
asked Aug 7 at 17:05
Gödel
1,145319
1,145319
I think you meant "transcendental over $F$". As to your collection, it isn't clear what you mean. If $f,gin F[x]$ then $lambda f, lambda g$ define the same element of $F(alpha)$. And if you allow multiple expressions for the same element then your collection defines $F(alpha)$ even if $alpha $ is algebraic.
– lulu
Aug 7 at 17:10
add a comment |Â
I think you meant "transcendental over $F$". As to your collection, it isn't clear what you mean. If $f,gin F[x]$ then $lambda f, lambda g$ define the same element of $F(alpha)$. And if you allow multiple expressions for the same element then your collection defines $F(alpha)$ even if $alpha $ is algebraic.
– lulu
Aug 7 at 17:10
I think you meant "transcendental over $F$". As to your collection, it isn't clear what you mean. If $f,gin F[x]$ then $lambda f, lambda g$ define the same element of $F(alpha)$. And if you allow multiple expressions for the same element then your collection defines $F(alpha)$ even if $alpha $ is algebraic.
– lulu
Aug 7 at 17:10
I think you meant "transcendental over $F$". As to your collection, it isn't clear what you mean. If $f,gin F[x]$ then $lambda f, lambda g$ define the same element of $F(alpha)$. And if you allow multiple expressions for the same element then your collection defines $F(alpha)$ even if $alpha $ is algebraic.
– lulu
Aug 7 at 17:10
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2875166%2felements-over-transcendental-extension%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
I think you meant "transcendental over $F$". As to your collection, it isn't clear what you mean. If $f,gin F[x]$ then $lambda f, lambda g$ define the same element of $F(alpha)$. And if you allow multiple expressions for the same element then your collection defines $F(alpha)$ even if $alpha $ is algebraic.
– lulu
Aug 7 at 17:10