Show that $M$ can be generated by the maximal ideals in a Noetherian semilocal ring.
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Let $R$ be a Noetherian semilocal ring and $M$ a finite $R$-module.
Write $n=max{mu_{R_m}(M_m)|min m-text{Spec}(R)}$. Show that $M$ can be generated by $n$ elements.
Doesn't this come directly from the definition of a semilocal ring and the fact that $M$ is finite?
commutative-algebra
asked Nov 13 at 21:35
Username Unknown
1,21341954
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up vote
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Let $R$ be a Noetherian semilocal ring and $M$ a finite $R$-module.
Write $n=max{mu_{R_m}(M_m)|min m-text{Spec}(R)}$. Show that $M$ can be generated by $n$ elements.
Doesn't this come directly from the definition of a semilocal ring and the fact that $M$ is finite?
commutative-algebra
asked Nov 13 at 21:35
Username Unknown
1,21341954
The question is too vague. Please tell us your argument and then some one can tell you whether you are missing something.
– Mohan
Nov 14 at 1:55
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Let $R$ be a Noetherian semilocal ring and $M$ a finite $R$-module.
Write $n=max{mu_{R_m}(M_m)|min m-text{Spec}(R)}$. Show that $M$ can be generated by $n$ elements.
Doesn't this come directly from the definition of a semilocal ring and the fact that $M$ is finite?
commutative-algebra
asked Nov 13 at 21:35
Username Unknown
1,21341954
Let $R$ be a Noetherian semilocal ring and $M$ a finite $R$-module.
Write $n=max{mu_{R_m}(M_m)|min m-text{Spec}(R)}$. Show that $M$ can be generated by $n$ elements.
Doesn't this come directly from the definition of a semilocal ring and the fact that $M$ is finite?
commutative-algebra
commutative-algebra
asked Nov 13 at 21:35
Username Unknown
1,21341954
asked Nov 13 at 21:35
Username Unknown
1,21341954
asked Nov 13 at 21:35
Username Unknown
1,21341954
asked Nov 13 at 21:35
Username Unknown
1,21341954
asked Nov 13 at 21:35
Username Unknown
1,21341954
1,21341954
The question is too vague. Please tell us your argument and then some one can tell you whether you are missing something.
– Mohan
Nov 14 at 1:55
add a comment |
The question is too vague. Please tell us your argument and then some one can tell you whether you are missing something.
– Mohan
Nov 14 at 1:55
The question is too vague. Please tell us your argument and then some one can tell you whether you are missing something.
– Mohan
Nov 14 at 1:55
The question is too vague. Please tell us your argument and then some one can tell you whether you are missing something.
– Mohan
Nov 14 at 1:55
add a comment |
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The question is too vague. Please tell us your argument and then some one can tell you whether you are missing something.
– Mohan
Nov 14 at 1:55