Mixing
Ideals with equal squares in a Noetherian UFD of dimension 2
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Let $I$ and $J$ be two ideals in $mathbb C[X,Y]$ such that $mu(I)=mu(J) le 3$ and $I^2=J^2$ . Then is it necessarily true that $I=J$ ? If not, then is it at least true if we assume $I,J$ are homogeneous ideals ?
I believe it should not be true but I am having a hard time finding a counterexample.
Please help
ring-theory commutative-algebra noetherian unique-factorization-domains primary-decomposition
asked Jan 30 at 2:03
user102248user102248
30619
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add a comment |
$begingroup$
Let $I$ and $J$ be two ideals in $mathbb C[X,Y]$ such that $mu(I)=mu(J) le 3$ and $I^2=J^2$ . Then is it necessarily true that $I=J$ ? If not, then is it at least true if we assume $I,J$ are homogeneous ideals ?
I believe it should not be true but I am having a hard time finding a counterexample.
Please help
ring-theory commutative-algebra noetherian unique-factorization-domains primary-decomposition
asked Jan 30 at 2:03
user102248user102248
30619
$endgroup$
$begingroup$
It sounds interesting, and there is another question similar to this. Where does this question come from?
$endgroup$
– Youngsu
Feb 6 at 6:07
add a comment |
$begingroup$
Let $I$ and $J$ be two ideals in $mathbb C[X,Y]$ such that $mu(I)=mu(J) le 3$ and $I^2=J^2$ . Then is it necessarily true that $I=J$ ? If not, then is it at least true if we assume $I,J$ are homogeneous ideals ?
I believe it should not be true but I am having a hard time finding a counterexample.
Please help
ring-theory commutative-algebra noetherian unique-factorization-domains primary-decomposition
asked Jan 30 at 2:03
user102248user102248
30619
$endgroup$
Let $I$ and $J$ be two ideals in $mathbb C[X,Y]$ such that $mu(I)=mu(J) le 3$ and $I^2=J^2$ . Then is it necessarily true that $I=J$ ? If not, then is it at least true if we assume $I,J$ are homogeneous ideals ?
I believe it should not be true but I am having a hard time finding a counterexample.
Please help
ring-theory commutative-algebra noetherian unique-factorization-domains primary-decomposition
ring-theory commutative-algebra noetherian unique-factorization-domains primary-decomposition
asked Jan 30 at 2:03
user102248user102248
30619
asked Jan 30 at 2:03
user102248user102248
30619
edited Feb 13 at 22:30
user102248
asked Jan 30 at 2:03
user102248user102248
30619
asked Jan 30 at 2:03
user102248user102248
30619
asked Jan 30 at 2:03
user102248user102248
30619
30619
$begingroup$
It sounds interesting, and there is another question similar to this. Where does this question come from?
$endgroup$
– Youngsu
Feb 6 at 6:07
add a comment |
$begingroup$
It sounds interesting, and there is another question similar to this. Where does this question come from?
$endgroup$
– Youngsu
Feb 6 at 6:07
$begingroup$
It sounds interesting, and there is another question similar to this. Where does this question come from?
$endgroup$
– Youngsu
Feb 6 at 6:07
$begingroup$
It sounds interesting, and there is another question similar to this. Where does this question come from?
$endgroup$
– Youngsu
Feb 6 at 6:07
add a comment |
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$begingroup$
It sounds interesting, and there is another question similar to this. Where does this question come from?
$endgroup$
– Youngsu
Feb 6 at 6:07