Residue fields of $mathbb Z[X_1,…,X_n]$ are always finite ? [duplicate]
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Fields finitely generated as $mathbb Z$-algebras are finite?
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Let $mathfrak m$ be a maximal ideal of $mathbb Z[X_1,...,X_n]$;
then is it necessarily true that $mathbb Z[X_1,...,X_n]/mathfrak m$ is finite ?
polynomials ring-theory commutative-algebra field-theory maximal-and-prime-ideals
asked Dec 5 at 0:03
user521337
5201113
marked as duplicate by user26857 commutative-algebra
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Dec 5 at 14:54
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Fields finitely generated as $mathbb Z$-algebras are finite?
4 answers
Let $mathfrak m$ be a maximal ideal of $mathbb Z[X_1,...,X_n]$;
then is it necessarily true that $mathbb Z[X_1,...,X_n]/mathfrak m$ is finite ?
polynomials ring-theory commutative-algebra field-theory maximal-and-prime-ideals
asked Dec 5 at 0:03
user521337
5201113
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Dec 5 at 14:54
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up vote
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This question already has an answer here:
Fields finitely generated as $mathbb Z$-algebras are finite?
4 answers
Let $mathfrak m$ be a maximal ideal of $mathbb Z[X_1,...,X_n]$;
then is it necessarily true that $mathbb Z[X_1,...,X_n]/mathfrak m$ is finite ?
polynomials ring-theory commutative-algebra field-theory maximal-and-prime-ideals
asked Dec 5 at 0:03
user521337
5201113
This question already has an answer here:
Fields finitely generated as $mathbb Z$-algebras are finite?
4 answers
Let $mathfrak m$ be a maximal ideal of $mathbb Z[X_1,...,X_n]$;
then is it necessarily true that $mathbb Z[X_1,...,X_n]/mathfrak m$ is finite ?
This question already has an answer here:
Fields finitely generated as $mathbb Z$-algebras are finite?
4 answers
polynomials ring-theory commutative-algebra field-theory maximal-and-prime-ideals
polynomials ring-theory commutative-algebra field-theory maximal-and-prime-ideals
asked Dec 5 at 0:03
user521337
5201113
asked Dec 5 at 0:03
user521337
5201113
asked Dec 5 at 0:03
user521337
5201113
asked Dec 5 at 0:03
user521337
5201113
asked Dec 5 at 0:03
user521337
5201113
5201113
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Dec 5 at 14:54
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Yes, it follows from Zariski's lemma.
answered Dec 5 at 0:20
xyzzyz
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could you please care to elaborate ?
– user521337
Dec 5 at 0:33
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1 Answer
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1 Answer
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up vote
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Yes, it follows from Zariski's lemma.
answered Dec 5 at 0:20
xyzzyz
5,5331221
could you please care to elaborate ?
– user521337
Dec 5 at 0:33
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up vote
0
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Yes, it follows from Zariski's lemma.
answered Dec 5 at 0:20
xyzzyz
5,5331221
could you please care to elaborate ?
– user521337
Dec 5 at 0:33
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up vote
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up vote
0
down vote
Yes, it follows from Zariski's lemma.
answered Dec 5 at 0:20
xyzzyz
5,5331221
Yes, it follows from Zariski's lemma.
answered Dec 5 at 0:20
xyzzyz
5,5331221
answered Dec 5 at 0:20
xyzzyz
5,5331221
answered Dec 5 at 0:20
xyzzyz
5,5331221
answered Dec 5 at 0:20
xyzzyz
5,5331221
5,5331221
could you please care to elaborate ?
– user521337
Dec 5 at 0:33
add a comment |
could you please care to elaborate ?
– user521337
Dec 5 at 0:33
could you please care to elaborate ?
– user521337
Dec 5 at 0:33
could you please care to elaborate ?
– user521337
Dec 5 at 0:33
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