Realizable Hopf orders in \(KC_{p^3}\). (Q934058)
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scientific article; zbMATH DE number 5304620
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Realizable Hopf orders in \(KC_{p^3}\). |
scientific article; zbMATH DE number 5304620 |
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Realizable Hopf orders in \(KC_{p^3}\). (English)
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29 July 2008
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Let \(K\) be a finite field extension of \(\mathbb{Q}_p\) for a rational prime \(p\), and let \(KC\) be a group algebra for a cyclic group \(C\) of order \(p^3\). The author constructs a new class of Hopf orders in \(KC\) and determines when they are realizable by a Galois extension of \(K\). The paper continues previous efforts [see, e.g., \textit{R. G. Underwood} and \textit{L. N. Childs}, Trans. Am. Math. Soc. 358, No. 3, 1117-1163 (2006; Zbl 1084.16013)] to classify Hopf orders in \(KC\).
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discrete valuation rings
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cyclic groups
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Hopf orders
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realizability
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Galois modules
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group algebras
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