Prove that $M$ is generated by $p+n$ elements. [on hold]Finitely-generated $k$-algebras and their relationship with affine coordinate ringsMaximal ideals in rings of polynomialsIdeal Generated by Three Elements in Polynomial RingMaximal ideal in a polynomial ring over a field that is not algebraically closedHow to prove that an ideal can not be generated by 2 elementsA question on finitely generated $k$ algebraHow do we find ideals the ring $mathbb R[X_0, X_1, …, X_n,…]$? How do we show that each of these ideals are not finitely generated?Prove that $mathcal I (H) = (F_1 cdot F_2 cdots F_s).$Show that there exist $a,b in K [X_1,X_2,cdots,X_n]$ and $d in K[X_1,X_2,cdots,X_n-1]$ such that $aF+bG = d.$Prove that any closed irreducible subset of $mathrm Spec (R)$ has a unique generic point.
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Prove that $M$ is generated by $p+n$ elements. [on hold]
Finitely-generated $k$-algebras and their relationship with affine coordinate ringsMaximal ideals in rings of polynomialsIdeal Generated by Three Elements in Polynomial RingMaximal ideal in a polynomial ring over a field that is not algebraically closedHow to prove that an ideal can not be generated by 2 elementsA question on finitely generated $k$ algebraHow do we find ideals the ring $mathbb R[X_0, X_1, …, X_n,…]$? How do we show that each of these ideals are not finitely generated?Prove that $mathcal I (H) = (F_1 cdot F_2 cdots F_s).$Show that there exist $a,b in K [X_1,X_2,cdots,X_n]$ and $d in K[X_1,X_2,cdots,X_n-1]$ such that $aF+bG = d.$Prove that any closed irreducible subset of $mathrm Spec (R)$ has a unique generic point.
$begingroup$
Let $R$ be a ring $,$ $M subseteq R[X_1, cdots ,X_n]$ a maximal ideal for which $M cap R$ is a maximal ideal of $R$ generated by $p$ elements. Then $M$ is generated by $p + n$ elements.
How do I proceed to prove it. Please help me in this regard.
Thank you very much.
algebraic-geometry commutative-algebra proof-writing
asked Mar 11 at 20:22
math maniac.math maniac.
475
$endgroup$
put on hold as off-topic by KReiser, Lee David Chung Lin, user26857, Leucippus, Chris Godsil Mar 12 at 1:31
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – KReiser, Lee David Chung Lin, user26857, Leucippus, Chris Godsil
add a comment |
$begingroup$
Let $R$ be a ring $,$ $M subseteq R[X_1, cdots ,X_n]$ a maximal ideal for which $M cap R$ is a maximal ideal of $R$ generated by $p$ elements. Then $M$ is generated by $p + n$ elements.
How do I proceed to prove it. Please help me in this regard.
Thank you very much.
algebraic-geometry commutative-algebra proof-writing
asked Mar 11 at 20:22
math maniac.math maniac.
475
$endgroup$
put on hold as off-topic by KReiser, Lee David Chung Lin, user26857, Leucippus, Chris Godsil Mar 12 at 1:31
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – KReiser, Lee David Chung Lin, user26857, Leucippus, Chris Godsil
1
$begingroup$
Have you tried anything so far? Where have you gotten stuck?
$endgroup$
– KReiser
Mar 11 at 20:29
$begingroup$
Can you give me some hint to proceed @KReiser?
$endgroup$
– math maniac.
Mar 11 at 20:38
$begingroup$
Hint (for $n=1$). Set $m=Mcap R$. Then $m[X]subsetneq M$, and $M/m[X]$ is a maximal ideal in a polynomial ring over a field.
$endgroup$
– user26857
Mar 11 at 21:58
add a comment |
$begingroup$
Let $R$ be a ring $,$ $M subseteq R[X_1, cdots ,X_n]$ a maximal ideal for which $M cap R$ is a maximal ideal of $R$ generated by $p$ elements. Then $M$ is generated by $p + n$ elements.
How do I proceed to prove it. Please help me in this regard.
Thank you very much.
algebraic-geometry commutative-algebra proof-writing
asked Mar 11 at 20:22
math maniac.math maniac.
475
$endgroup$
Let $R$ be a ring $,$ $M subseteq R[X_1, cdots ,X_n]$ a maximal ideal for which $M cap R$ is a maximal ideal of $R$ generated by $p$ elements. Then $M$ is generated by $p + n$ elements.
How do I proceed to prove it. Please help me in this regard.
Thank you very much.
algebraic-geometry commutative-algebra proof-writing
algebraic-geometry commutative-algebra proof-writing
asked Mar 11 at 20:22
math maniac.math maniac.
475
asked Mar 11 at 20:22
math maniac.math maniac.
475
asked Mar 11 at 20:22
math maniac.math maniac.
475
asked Mar 11 at 20:22
math maniac.math maniac.
475
asked Mar 11 at 20:22
math maniac.math maniac.
475
475
put on hold as off-topic by KReiser, Lee David Chung Lin, user26857, Leucippus, Chris Godsil Mar 12 at 1:31
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – KReiser, Lee David Chung Lin, user26857, Leucippus, Chris Godsil
put on hold as off-topic by KReiser, Lee David Chung Lin, user26857, Leucippus, Chris Godsil Mar 12 at 1:31
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – KReiser, Lee David Chung Lin, user26857, Leucippus, Chris Godsil
1
$begingroup$
Have you tried anything so far? Where have you gotten stuck?
$endgroup$
– KReiser
Mar 11 at 20:29
$begingroup$
Can you give me some hint to proceed @KReiser?
$endgroup$
– math maniac.
Mar 11 at 20:38
$begingroup$
Hint (for $n=1$). Set $m=Mcap R$. Then $m[X]subsetneq M$, and $M/m[X]$ is a maximal ideal in a polynomial ring over a field.
$endgroup$
– user26857
Mar 11 at 21:58
add a comment |
1
$begingroup$
Have you tried anything so far? Where have you gotten stuck?
$endgroup$
– KReiser
Mar 11 at 20:29
$begingroup$
Can you give me some hint to proceed @KReiser?
$endgroup$
– math maniac.
Mar 11 at 20:38
$begingroup$
Hint (for $n=1$). Set $m=Mcap R$. Then $m[X]subsetneq M$, and $M/m[X]$ is a maximal ideal in a polynomial ring over a field.
$endgroup$
– user26857
Mar 11 at 21:58
1
1
$begingroup$
Have you tried anything so far? Where have you gotten stuck?
$endgroup$
– KReiser
Mar 11 at 20:29
$begingroup$
Have you tried anything so far? Where have you gotten stuck?
$endgroup$
– KReiser
Mar 11 at 20:29
$begingroup$
Can you give me some hint to proceed @KReiser?
$endgroup$
– math maniac.
Mar 11 at 20:38
$begingroup$
Can you give me some hint to proceed @KReiser?
$endgroup$
– math maniac.
Mar 11 at 20:38
$begingroup$
Hint (for $n=1$). Set $m=Mcap R$. Then $m[X]subsetneq M$, and $M/m[X]$ is a maximal ideal in a polynomial ring over a field.
$endgroup$
– user26857
Mar 11 at 21:58
$begingroup$
Hint (for $n=1$). Set $m=Mcap R$. Then $m[X]subsetneq M$, and $M/m[X]$ is a maximal ideal in a polynomial ring over a field.
$endgroup$
– user26857
Mar 11 at 21:58
add a comment |
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$begingroup$
Have you tried anything so far? Where have you gotten stuck?
$endgroup$
– KReiser
Mar 11 at 20:29
$begingroup$
Can you give me some hint to proceed @KReiser?
$endgroup$
– math maniac.
Mar 11 at 20:38
$begingroup$
Hint (for $n=1$). Set $m=Mcap R$. Then $m[X]subsetneq M$, and $M/m[X]$ is a maximal ideal in a polynomial ring over a field.
$endgroup$
– user26857
Mar 11 at 21:58