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Show that $f(x)$ is a power of $operatornameirr(α, F)$, and $f(x) = operatornameirr(α, F) iff K = F(α)$.

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0

1

$begingroup$

Let $K$ be a finite normal extension of $F$.

$f(x)=prod_sigma in G(E/F) (x − sigma(alpha))$ where $f(x)in F[x]$

How can I show that $f(x)$ is a power of $operatornameirr(α, F)$ and $f(x) = operatornameirr(α, F) iff K = F(α)$ ?

abstract-algebra galois-theory galois-extensions

share|cite|improve this question

edited 21 hours ago

Andrews

1,2812422

asked yesterday

bensimmonsisarookiebensimmonsisarookie

83

$endgroup$

add a comment | 

0

1

$begingroup$

Let $K$ be a finite normal extension of $F$.

$f(x)=prod_sigma in G(E/F) (x − sigma(alpha))$ where $f(x)in F[x]$

How can I show that $f(x)$ is a power of $operatornameirr(α, F)$ and $f(x) = operatornameirr(α, F) iff K = F(α)$ ?

abstract-algebra galois-theory galois-extensions

share|cite|improve this question

edited 21 hours ago

Andrews

1,2812422

asked yesterday

bensimmonsisarookiebensimmonsisarookie

83

$endgroup$

add a comment | 

$begingroup$

Let $K$ be a finite normal extension of $F$.

$f(x)=prod_sigma in G(E/F) (x − sigma(alpha))$ where $f(x)in F[x]$

How can I show that $f(x)$ is a power of $operatornameirr(α, F)$ and $f(x) = operatornameirr(α, F) iff K = F(α)$ ?

abstract-algebra galois-theory galois-extensions

share|cite|improve this question

edited 21 hours ago

Andrews

1,2812422

asked yesterday

bensimmonsisarookiebensimmonsisarookie

83

$endgroup$

share|cite|improve this question

edited 21 hours ago

Andrews

1,2812422

asked yesterday

bensimmonsisarookiebensimmonsisarookie

83

share|cite|improve this question

edited 21 hours ago

Andrews

1,2812422

asked yesterday

bensimmonsisarookiebensimmonsisarookie

83

edited 21 hours ago

Andrews

1,2812422

edited 21 hours ago

Andrews

1,2812422

asked yesterday

bensimmonsisarookiebensimmonsisarookie

83

asked yesterday

bensimmonsisarookiebensimmonsisarookie

83