Mixing
Length of a module is sum of length of modules localization at each associated prime.
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Let $M$ be an $A$ module with length of the module $M,$ i.e., $ell_{A}(M)< infty .$ Also the $A$ be a Noetherian ring. Then I want to show that $ell_{A}(M)= sum_{p in text{Ass}(M)} ell_{A_p}(M_p).$
I was trying to show this if $text{Ass}(M) $ is singleton. I couldn't do much. I need some help. Thank you.
abstract-algebra commutative-algebra modules primary-decomposition
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user371231
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up vote
1
down vote
favorite
Let $M$ be an $A$ module with length of the module $M,$ i.e., $ell_{A}(M)< infty .$ Also the $A$ be a Noetherian ring. Then I want to show that $ell_{A}(M)= sum_{p in text{Ass}(M)} ell_{A_p}(M_p).$
I was trying to show this if $text{Ass}(M) $ is singleton. I couldn't do much. I need some help. Thank you.
abstract-algebra commutative-algebra modules primary-decomposition
asked 2 hours ago
user371231
521510
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Let $M$ be an $A$ module with length of the module $M,$ i.e., $ell_{A}(M)< infty .$ Also the $A$ be a Noetherian ring. Then I want to show that $ell_{A}(M)= sum_{p in text{Ass}(M)} ell_{A_p}(M_p).$
I was trying to show this if $text{Ass}(M) $ is singleton. I couldn't do much. I need some help. Thank you.
abstract-algebra commutative-algebra modules primary-decomposition
asked 2 hours ago
user371231
521510
Let $M$ be an $A$ module with length of the module $M,$ i.e., $ell_{A}(M)< infty .$ Also the $A$ be a Noetherian ring. Then I want to show that $ell_{A}(M)= sum_{p in text{Ass}(M)} ell_{A_p}(M_p).$
I was trying to show this if $text{Ass}(M) $ is singleton. I couldn't do much. I need some help. Thank you.
abstract-algebra commutative-algebra modules primary-decomposition
abstract-algebra commutative-algebra modules primary-decomposition
asked 2 hours ago
user371231
521510
asked 2 hours ago
user371231
521510
asked 2 hours ago
user371231
521510
asked 2 hours ago
user371231
521510
asked 2 hours ago
user371231
521510
521510
add a comment |
add a comment |
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