Prime to p extensions of the generic abelian crossed product

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Abstract

In this paper we prove that the non-cyclic generic abelian crossed product p-algebras constructed by Amitsur and Saltman in [S.A. Amitsur, D. Saltman, Generic Abelian crossed products and p-algebras, J. Algebra 51 (1) (1978) 76-87] remain non-cyclic after tensoring by any prime to p extension of their centers. We also prove that an example due to Saltman of an indecomposable generic abelian crossed product with exponent p and degree p2 remains indecomposable after any prime to p extension.

Original languageEnglish
Pages (from-to)813-832
Number of pages20
JournalJournal of Algebra
Volume317
Issue number2
DOIs
StatePublished - Nov 15 2007

Keywords

  • Cyclic algebras
  • Division algebras
  • Indecomposable division algebras
  • Valuation theory
  • p-Algebras

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