Mixing
Prime ideals in $R[X]/I$
0
$begingroup$
How many prime ideals do we have in $R[X]/I$ if $I =⟨(X^2 − 1)^5⟩$ ???
group-theory ring-theory ideals maximal-and-prime-ideals
asked Jan 16 at 22:43
Juan SoloJuan Solo
1
$endgroup$
add a comment |
0
$begingroup$
How many prime ideals do we have in $R[X]/I$ if $I =⟨(X^2 − 1)^5⟩$ ???
group-theory ring-theory ideals maximal-and-prime-ideals
asked Jan 16 at 22:43
Juan SoloJuan Solo
1
$endgroup$
2
$begingroup$
What have you tried so far? Can you find out all the ideals of this ring?
$endgroup$
– Mindlack
Jan 16 at 22:46
$begingroup$
I don't know how to. Any good recommendation for it?
$endgroup$
– Juan Solo
Jan 16 at 22:48
$begingroup$
Prove that all ideals are the images of some $(P)$, where $P$ is some divisor of $(X^2-1)^5$. Prove that the ideal is prime iff $P$ is irreducible.
$endgroup$
– Mindlack
Jan 16 at 22:49
$begingroup$
I've got that there are 36 possible ideals, but I can't decide which of them are irreducibles ( i've just noticed that those ideals of degree 0 or 1 (3 in total) are irreducibles)
$endgroup$
– Juan Solo
Jan 16 at 23:00
add a comment |
0
0
0
0
$begingroup$
How many prime ideals do we have in $R[X]/I$ if $I =⟨(X^2 − 1)^5⟩$ ???
group-theory ring-theory ideals maximal-and-prime-ideals
asked Jan 16 at 22:43
Juan SoloJuan Solo
1
$endgroup$
How many prime ideals do we have in $R[X]/I$ if $I =⟨(X^2 − 1)^5⟩$ ???
group-theory ring-theory ideals maximal-and-prime-ideals
group-theory ring-theory ideals maximal-and-prime-ideals
asked Jan 16 at 22:43
Juan SoloJuan Solo
1
asked Jan 16 at 22:43
Juan SoloJuan Solo
1
asked Jan 16 at 22:43
Juan SoloJuan Solo
1
asked Jan 16 at 22:43
Juan SoloJuan Solo
1
asked Jan 16 at 22:43
Juan SoloJuan Solo
1
1
2
$begingroup$
What have you tried so far? Can you find out all the ideals of this ring?
$endgroup$
– Mindlack
Jan 16 at 22:46
$begingroup$
I don't know how to. Any good recommendation for it?
$endgroup$
– Juan Solo
Jan 16 at 22:48
$begingroup$
Prove that all ideals are the images of some $(P)$, where $P$ is some divisor of $(X^2-1)^5$. Prove that the ideal is prime iff $P$ is irreducible.
$endgroup$
– Mindlack
Jan 16 at 22:49
$begingroup$
I've got that there are 36 possible ideals, but I can't decide which of them are irreducibles ( i've just noticed that those ideals of degree 0 or 1 (3 in total) are irreducibles)
$endgroup$
– Juan Solo
Jan 16 at 23:00
add a comment |
2
$begingroup$
What have you tried so far? Can you find out all the ideals of this ring?
$endgroup$
– Mindlack
Jan 16 at 22:46
$begingroup$
I don't know how to. Any good recommendation for it?
$endgroup$
– Juan Solo
Jan 16 at 22:48
$begingroup$
Prove that all ideals are the images of some $(P)$, where $P$ is some divisor of $(X^2-1)^5$. Prove that the ideal is prime iff $P$ is irreducible.
$endgroup$
– Mindlack
Jan 16 at 22:49
$begingroup$
I've got that there are 36 possible ideals, but I can't decide which of them are irreducibles ( i've just noticed that those ideals of degree 0 or 1 (3 in total) are irreducibles)
$endgroup$
– Juan Solo
Jan 16 at 23:00
2
2
$begingroup$
What have you tried so far? Can you find out all the ideals of this ring?
$endgroup$
– Mindlack
Jan 16 at 22:46
$begingroup$
What have you tried so far? Can you find out all the ideals of this ring?
$endgroup$
– Mindlack
Jan 16 at 22:46
$begingroup$
I don't know how to. Any good recommendation for it?
$endgroup$
– Juan Solo
Jan 16 at 22:48
$begingroup$
I don't know how to. Any good recommendation for it?
$endgroup$
– Juan Solo
Jan 16 at 22:48
$begingroup$
Prove that all ideals are the images of some $(P)$, where $P$ is some divisor of $(X^2-1)^5$. Prove that the ideal is prime iff $P$ is irreducible.
$endgroup$
– Mindlack
Jan 16 at 22:49
$begingroup$
Prove that all ideals are the images of some $(P)$, where $P$ is some divisor of $(X^2-1)^5$. Prove that the ideal is prime iff $P$ is irreducible.
$endgroup$
– Mindlack
Jan 16 at 22:49
$begingroup$
I've got that there are 36 possible ideals, but I can't decide which of them are irreducibles ( i've just noticed that those ideals of degree 0 or 1 (3 in total) are irreducibles)
$endgroup$
– Juan Solo
Jan 16 at 23:00
$begingroup$
I've got that there are 36 possible ideals, but I can't decide which of them are irreducibles ( i've just noticed that those ideals of degree 0 or 1 (3 in total) are irreducibles)
$endgroup$
– Juan Solo
Jan 16 at 23:00
add a comment |
0
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2
$begingroup$
What have you tried so far? Can you find out all the ideals of this ring?
$endgroup$
– Mindlack
Jan 16 at 22:46
$begingroup$
I don't know how to. Any good recommendation for it?
$endgroup$
– Juan Solo
Jan 16 at 22:48
$begingroup$
Prove that all ideals are the images of some $(P)$, where $P$ is some divisor of $(X^2-1)^5$. Prove that the ideal is prime iff $P$ is irreducible.
$endgroup$
– Mindlack
Jan 16 at 22:49
$begingroup$
I've got that there are 36 possible ideals, but I can't decide which of them are irreducibles ( i've just noticed that those ideals of degree 0 or 1 (3 in total) are irreducibles)
$endgroup$
– Juan Solo
Jan 16 at 23:00