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edit approved Sep 3, 2014 at 17:53
user26857
edit approved Sep 3, 2014 at 17:53
user26857
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When quotients of polynomial rings are isomorphic to polynomial rings?

This might be a silly question but is there a criterion for when the quotient of $k[X_1,\ldots, X_n]$ by some ideal is isomorphic to a polynomial ring?

This might be a silly question but is there a criterion for when the quotient of $k[X_1,\ldots, X_n]$ by some ideal is isomorphic to a polynomial ring? For instance $k[X,Y]/\langle Y \rangle \simeq k [X]$ but $k[X,Y]/\langle Y^2 \rangle$ is not a polynomial ring.

quotients of polynomial rings

This might be a silly question but is there a criterion for when the quotient of $k[X_1,\ldots, X_n]$ by some ideal is isomorphic to a polynomial ring? For instance $k[X,Y]/\langle Y \rangle \simeq k [X]$ but $k[X,Y]/\langle Y^2 \rangle$ is not a polynomial ring.

When quotients of polynomial rings are isomorphic to polynomial rings?

This might be a silly question but is there a criterion for when the quotient of $k[X_1,\ldots, X_n]$ by some ideal is isomorphic to a polynomial ring?

For instance $k[X,Y]/\langle Y \rangle \simeq k [X]$ but $k[X,Y]/\langle Y^2 \rangle$ is not a polynomial ring.

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Richard Stanley
Richard Stanley
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This might be a silly question but is there a criterion for when the quotient of $k[X_1,\ldots, X_n$$k[X_1,\ldots, X_n]$ by some ideal is isomorphic to a polynomial ring? For instance $k[X,Y]/\langle Y \rangle \simeq k [X]$ but $k[X,Y]/\langle Y^2 \rangle$ is not a polynomial ring.

This might be a silly question but is there a criterion for when the quotient of $k[X_1,\ldots, X_n$ by some ideal is isomorphic to a polynomial ring? For instance $k[X,Y]/\langle Y \rangle \simeq k [X]$ but $k[X,Y]/\langle Y^2 \rangle$ is not a polynomial ring.

This might be a silly question but is there a criterion for when the quotient of $k[X_1,\ldots, X_n]$ by some ideal is isomorphic to a polynomial ring? For instance $k[X,Y]/\langle Y \rangle \simeq k [X]$ but $k[X,Y]/\langle Y^2 \rangle$ is not a polynomial ring.

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Alex
Alex
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quotients of polynomial rings

This might be a silly question but is there a criterion for when the quotient of $k[X_1,\ldots, X_n$ by some ideal is isomorphic to a polynomial ring? For instance $k[X,Y]/\langle Y \rangle \simeq k [X]$ but $k[X,Y]/\langle Y^2 \rangle$ is not a polynomial ring.