On a subset of the associated primes of tensor product of modulesSet of associated primes of direct sumTensor product of faithful modulesTensor product of a module and a projective module.Tensor product of Noetherian modulesAssociated Primes of Tensor ProductAssociated primes of quotient modulePseudo associated primes and short exact sequencesTensor product of free modules over free algebratensor product of modules over commutative ringProjective and flat vs. faithfully flat
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On a subset of the associated primes of tensor product of modules
Set of associated primes of direct sumTensor product of faithful modulesTensor product of a module and a projective module.Tensor product of Noetherian modulesAssociated Primes of Tensor ProductAssociated primes of quotient modulePseudo associated primes and short exact sequencesTensor product of free modules over free algebratensor product of modules over commutative ringProjective and flat vs. faithfully flat
$begingroup$
For a module $M$ over a commutative ring $R$, let
$operatornameAss_R (M):=operatornameann_R (m) mid min M$ and $operatornameann_R(m) in operatornameSpec(R)$.
If $M,N$ are finitely generated $R$-modules and $P in operatornameAss_R(M)$, then is it true that $operatornameAss_R(N/PN)subseteq operatornameAss_R(M otimes_R N) $ ?
ring-theory commutative-algebra modules tensor-products primary-decomposition
asked Mar 16 at 9:22
user521337user521337
1,2061417
$endgroup$
add a comment |
$begingroup$
For a module $M$ over a commutative ring $R$, let
$operatornameAss_R (M):=operatornameann_R (m) mid min M$ and $operatornameann_R(m) in operatornameSpec(R)$.
If $M,N$ are finitely generated $R$-modules and $P in operatornameAss_R(M)$, then is it true that $operatornameAss_R(N/PN)subseteq operatornameAss_R(M otimes_R N) $ ?
ring-theory commutative-algebra modules tensor-products primary-decomposition
asked Mar 16 at 9:22
user521337user521337
1,2061417
$endgroup$
$begingroup$
It's an interesting question, but what's the context? Why is this plausible, and what thoughts do you have on the question?
$endgroup$
– jgon
Mar 18 at 20:24
add a comment |
$begingroup$
For a module $M$ over a commutative ring $R$, let
$operatornameAss_R (M):=operatornameann_R (m) mid min M$ and $operatornameann_R(m) in operatornameSpec(R)$.
If $M,N$ are finitely generated $R$-modules and $P in operatornameAss_R(M)$, then is it true that $operatornameAss_R(N/PN)subseteq operatornameAss_R(M otimes_R N) $ ?
ring-theory commutative-algebra modules tensor-products primary-decomposition
asked Mar 16 at 9:22
user521337user521337
1,2061417
$endgroup$
For a module $M$ over a commutative ring $R$, let
$operatornameAss_R (M):=operatornameann_R (m) mid min M$ and $operatornameann_R(m) in operatornameSpec(R)$.
If $M,N$ are finitely generated $R$-modules and $P in operatornameAss_R(M)$, then is it true that $operatornameAss_R(N/PN)subseteq operatornameAss_R(M otimes_R N) $ ?
ring-theory commutative-algebra modules tensor-products primary-decomposition
ring-theory commutative-algebra modules tensor-products primary-decomposition
asked Mar 16 at 9:22
user521337user521337
1,2061417
asked Mar 16 at 9:22
user521337user521337
1,2061417
edited 2 days ago
user521337
asked Mar 16 at 9:22
user521337user521337
1,2061417
asked Mar 16 at 9:22
user521337user521337
1,2061417
asked Mar 16 at 9:22
user521337user521337
1,2061417
1,2061417
$begingroup$
It's an interesting question, but what's the context? Why is this plausible, and what thoughts do you have on the question?
$endgroup$
– jgon
Mar 18 at 20:24
add a comment |
$begingroup$
It's an interesting question, but what's the context? Why is this plausible, and what thoughts do you have on the question?
$endgroup$
– jgon
Mar 18 at 20:24
$begingroup$
It's an interesting question, but what's the context? Why is this plausible, and what thoughts do you have on the question?
$endgroup$
– jgon
Mar 18 at 20:24
$begingroup$
It's an interesting question, but what's the context? Why is this plausible, and what thoughts do you have on the question?
$endgroup$
– jgon
Mar 18 at 20:24
add a comment |
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$begingroup$
It's an interesting question, but what's the context? Why is this plausible, and what thoughts do you have on the question?
$endgroup$
– jgon
Mar 18 at 20:24