Purity and Gorenstein filtered rings. (Q2839631)
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scientific article; zbMATH DE number 6187541
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Purity and Gorenstein filtered rings. |
scientific article; zbMATH DE number 6187541 |
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12 July 2013
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Gorenstein filtered rings
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filtered modules
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good filtrations
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purities
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pure lengths
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0.89669895
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Purity and Gorenstein filtered rings. (English)
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The main aim of this manuscript is to define a notion of `pure length', denoted by \(\text{pl}(\cdot)\), and to generalize a theorem of \textit{J.-E. Björk} and \textit{E. K. Ekström} [in Operator algebras, unitary representations, enveloping algebras, and invariant theory, Prog. Math. 92, 425-448 (1990; Zbl 0733.16016), Theorem 1.1]. The author's attempt succeeds and he gets a good filtration of a filtered module \(M\) with \(\text{pl}(M)=\text{pl}(\text{gr}_{\mathcal F}M)\). When \(\text{pl}(M)=1\), \(M\) is pure and the theorem was proved by \textit{J. E. Björk} and \textit{E. K. Ekström} [loc. cit.]. The proposed new notion `pure length' works well.
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