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0

$begingroup$

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

share|cite|improve this question

edited 2 days ago

user521337

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 | 

0

$begingroup$

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

share|cite|improve this question

edited 2 days ago

user521337

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

share|cite|improve this question

edited 2 days ago

user521337

asked Mar 16 at 9:22

user521337user521337

1,2061417

$endgroup$

share|cite|improve this question

edited 2 days ago

user521337

asked Mar 16 at 9:22

user521337user521337

1,2061417

share|cite|improve this question

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