Prime to p extensions of the generic abelian crossed product

Kelly McKinnie

doi:10.1016/j.jalgebra.2007.07.018

Prime to p extensions of the generic abelian crossed product

Kelly McKinnie

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 language	English
Pages (from-to)	813-832
Number of pages	20
Journal	Journal of Algebra
Volume	317
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2007.07.018
State	Published - Nov 15 2007

Funding

1 The author is supported by an NSF Postdoctoral Research Fellowship. The work in this paper constitutes part of my doctoral thesis at the University of Texas at Austin. Part of this work was completed while I held a continuing education fellowship from the University of Texas at Austin and a VIGRE graduate research fellowship. I would like to thank my doctoral thesis advisor, Dr. David Saltman, for suggesting the problem to me and for many helpful conversations. I would also like to thank Adrian Wadsworth for reading an earlier draft of this paper and for many valuable suggestions.

Funders
University of Texas at Austin

Keywords

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

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10.1016/j.jalgebra.2007.07.018

Cite this

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title = "Prime to p extensions of the generic abelian crossed product",

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.",

keywords = "Cyclic algebras, Division algebras, Indecomposable division algebras, Valuation theory, p-Algebras",

author = "Kelly McKinnie",

note = "Funding Information: 1 The author is supported by an NSF Postdoctoral Research Fellowship. Funding Information: The work in this paper constitutes part of my doctoral thesis at the University of Texas at Austin. Part of this work was completed while I held a continuing education fellowship from the University of Texas at Austin and a VIGRE graduate research fellowship. I would like to thank my doctoral thesis advisor, Dr. David Saltman, for suggesting the problem to me and for many helpful conversations. I would also like to thank Adrian Wadsworth for reading an earlier draft of this paper and for many valuable suggestions.",

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N2 - 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.

AB - 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.

KW - Cyclic algebras

KW - Division algebras

KW - Indecomposable division algebras

KW - Valuation theory

KW - p-Algebras

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DO - 10.1016/j.jalgebra.2007.07.018

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VL - 317

SP - 813

EP - 832

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

Prime to p extensions of the generic abelian crossed product

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