Conjugate field [on hold]Algebraic Field ExtensionsA sufficient condition for irreducibility of a polynomial...
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Conjugate field [on hold]
Algebraic Field ExtensionsA sufficient condition for irreducibility of a polynomial in an extension field.All the isomorphisms of a finite algebraic separable field extensionDifference between algebraic and integral extensionAbout $K$-embeddings and the pertinence of an element of a finite and separable field extensionAbout some properties of composites of field extesionsDegree of a field extension is a power of 2Find the degree of the extension $Bbb R(theta)/Bbb R$Axiomatize purely transcendental field extensionDo extension fields always belong to a bigger field?
$begingroup$
Let $theta in C$ and $ K= Q(theta)$ be an algebraic number field of degree $n$. Let $theta_1 = theta, theta_2, theta_3,ldots,theta_n$ be the conjugates of $theta$ over $Q$. Suppose that there are exactly $m$ distinct fields among $Q(theta_1),Q(theta_2),ldots, Q(theta_n)$. Prove that $m | n$ and each field occurs $n/m$ times.
This is exercise in book about algebraic number theory.
extension-field
asked Mar 10 at 3:15
Quyet Nguyen VanQuyet Nguyen Van
11
New contributor
Quyet Nguyen Van is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
put on hold as off-topic by Servaes, Thomas Shelby, Vinyl_cape_jawa, Cesareo, José Carlos Santos Mar 10 at 10:25
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Servaes, Thomas Shelby, Vinyl_cape_jawa, Cesareo, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Let $theta in C$ and $ K= Q(theta)$ be an algebraic number field of degree $n$. Let $theta_1 = theta, theta_2, theta_3,ldots,theta_n$ be the conjugates of $theta$ over $Q$. Suppose that there are exactly $m$ distinct fields among $Q(theta_1),Q(theta_2),ldots, Q(theta_n)$. Prove that $m | n$ and each field occurs $n/m$ times.
This is exercise in book about algebraic number theory.
extension-field
asked Mar 10 at 3:15
Quyet Nguyen VanQuyet Nguyen Van
11
New contributor
Quyet Nguyen Van is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
put on hold as off-topic by Servaes, Thomas Shelby, Vinyl_cape_jawa, Cesareo, José Carlos Santos Mar 10 at 10:25
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Servaes, Thomas Shelby, Vinyl_cape_jawa, Cesareo, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Let $theta in C$ and $ K= Q(theta)$ be an algebraic number field of degree $n$. Let $theta_1 = theta, theta_2, theta_3,ldots,theta_n$ be the conjugates of $theta$ over $Q$. Suppose that there are exactly $m$ distinct fields among $Q(theta_1),Q(theta_2),ldots, Q(theta_n)$. Prove that $m | n$ and each field occurs $n/m$ times.
This is exercise in book about algebraic number theory.
extension-field
asked Mar 10 at 3:15
Quyet Nguyen VanQuyet Nguyen Van
11
New contributor
Quyet Nguyen Van is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Let $theta in C$ and $ K= Q(theta)$ be an algebraic number field of degree $n$. Let $theta_1 = theta, theta_2, theta_3,ldots,theta_n$ be the conjugates of $theta$ over $Q$. Suppose that there are exactly $m$ distinct fields among $Q(theta_1),Q(theta_2),ldots, Q(theta_n)$. Prove that $m | n$ and each field occurs $n/m$ times.
This is exercise in book about algebraic number theory.
extension-field
extension-field
asked Mar 10 at 3:15
Quyet Nguyen VanQuyet Nguyen Van
11
New contributor
Quyet Nguyen Van is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 10 at 3:15
Quyet Nguyen VanQuyet Nguyen Van
11
New contributor
Quyet Nguyen Van is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 10 at 3:15
Quyet Nguyen VanQuyet Nguyen Van
11
New contributor
Quyet Nguyen Van is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 10 at 3:15
Quyet Nguyen VanQuyet Nguyen Van
11
asked Mar 10 at 3:15
Quyet Nguyen VanQuyet Nguyen Van
11
11
New contributor
Quyet Nguyen Van is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Quyet Nguyen Van is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Quyet Nguyen Van is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Servaes, Thomas Shelby, Vinyl_cape_jawa, Cesareo, José Carlos Santos Mar 10 at 10:25
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Servaes, Thomas Shelby, Vinyl_cape_jawa, Cesareo, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Servaes, Thomas Shelby, Vinyl_cape_jawa, Cesareo, José Carlos Santos Mar 10 at 10:25
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Servaes, Thomas Shelby, Vinyl_cape_jawa, Cesareo, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
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