On the Krull dimension of noetherian rings (Q731909)
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scientific article; zbMATH DE number 5611747
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Krull dimension of noetherian rings |
scientific article; zbMATH DE number 5611747 |
Statements
On the Krull dimension of noetherian rings (English)
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9 October 2009
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Let \(R\) be a commutative ring, \(x\in R\), \(q_x\) the Krull dimension of \(R/(x)\), that is \(q_x=K\dim \;R/(x)\), and \(d_x=K\dim \;S^{-1}R\), where \(S\subset R\) is the multiplicative system generated by \(x\). It gives new proofs for the main results of dimension theory and it shows that \(K\dim\;R \leq \max(d_x,q_x)+ \delta_{d_x,q_x}\), \(\delta\) being Kronecker' symbol.
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noetherian rings
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Krull dimension
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Krull principal ideal theorem
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Bass' stable range theorem
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