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On the realization and classification of cyclic extensions of polynomial algebras over the Steenrod algebra


Authors: Howard Hiller and Larry Smith
Journal: Proc. Amer. Math. Soc. 100 (1987), 731-738
MSC: Primary 55S10
MathSciNet review: 894446
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Abstract: Suppose $ {{\mathbf{R}}^*}$ is an unstable algebra over the Steenrod algebra of the form $ {{\mathbf{P}}^*}(\sqrt[k]{d})$, where $ {{\mathbf{P}}^*}$ is a polynomial algebra over the Steenrod algebra. If $ {{\mathbf{R}}^*}$ is integrally closed then $ {{\mathbf{R}}^*} = P{(V)^{{G_\mathcal{X}}}}$, where $ C \leqslant GL(V)$ is generated by pseudoreflections and $ {G_\mathcal{X}} = \ker \{ \mathcal{X}:G \to {\mathbf{F}}_p^*\} $ is a character of degree $ k$.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0894446-9
Article copyright: © Copyright 1987 American Mathematical Society