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David Roberts ♦
David Roberts ♦
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Number of generators of an ideal in a polynomial ring over a Noetherian ring

Let $R$ be a noetherianNoetherian ring. By the Hilbert Basis Theorem the polinomialpolynomial ring $R[x_1, ... , x_n]$$R[x_1, \ldots , x_n]$ is also a noetherianNoetherian ring. What can we say about the number of generators of of an ideal $I$ of $R[x_1, ... , x_n]$$R[x_1, \ldots , x_n]$? (We can suppose that every ideal in $R$ is principal)

Noetherian ring

Let $R$ be a noetherian ring. By the Hilbert Basis Theorem the polinomial ring $R[x_1, ... , x_n]$ is also a noetherian ring. What can we say about the number of generators of an ideal $I$ of $R[x_1, ... , x_n]$? (We can suppose that every ideal in $R$ is principal)

Number of generators of an ideal in a polynomial ring over a Noetherian ring

Let $R$ be a Noetherian ring. By the Hilbert Basis Theorem the polynomial ring $R[x_1, \ldots , x_n]$ is also a Noetherian ring. What can we say about the number of generators of an ideal $I$ of $R[x_1, \ldots , x_n]$? (We can suppose that every ideal in $R$ is principal)

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Martin Brandenburg
Martin Brandenburg
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Let $R$ be a noetherian ring. By the Hilbert Basis Theorem the polinomial ring $R[x_1, ... , x_n]$ is also a noetherian ring. What can we say about the number of generators of an ideanideal $I$ of $R[x_1, ... , x_n]$? (We can suppose that every ideal in $R$ is principal)

Let $R$ be a noetherian ring. By the Hilbert Basis Theorem the polinomial ring $R[x_1, ... , x_n]$ is also a noetherian ring. What can we say about the number of generators of an idean $I$ of $R[x_1, ... , x_n]$? (We can suppose that every ideal in $R$ is principal)

Let $R$ be a noetherian ring. By the Hilbert Basis Theorem the polinomial ring $R[x_1, ... , x_n]$ is also a noetherian ring. What can we say about the number of generators of an ideal $I$ of $R[x_1, ... , x_n]$? (We can suppose that every ideal in $R$ is principal)

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Miguel
Miguel
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Noetherian ring

Let $R$ be a noetherian ring. By the Hilbert Basis Theorem the polinomial ring $R[x_1, ... , x_n]$ is also a noetherian ring. What can we say about the number of generators of an idean $I$ of $R[x_1, ... , x_n]$? (We can suppose that every ideal in $R$ is principal)