Coherent power series ring and weak Gorenstein global dimension (Q2845570)
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scientific article; zbMATH DE number 6203588
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Coherent power series ring and weak Gorenstein global dimension |
scientific article; zbMATH DE number 6203588 |
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2 September 2013
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Coherent power series ring and weak Gorenstein global dimension (English)
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Let \(R\) be a commutative unital ring. The authors show that if the ring \(R[\![x]\!]\) of formal power series with coefficients in \(R\) is coherent, then its weak Gorenstein global dimension is equal to the weak Gorenstein global dimension of \(R\) plus one. In symbols: \(\mathrm{wGgldim}(R[\![x]\!]) = \mathrm{wGgldim}(R) + 1\). This result is motivated by a similar result for (ordinary) weak global dimension due to \textit{S. Jøndrup} and \textit{L. W. Small} [Math. Scand. 35, 21--24 (1974; Zbl 0298.13015)].
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