Prime to p extensions of the generic abelian crossed product

[摘要] 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 p(2) remains indecomposable after any prime to p extension. (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-11-15

[关键词] division algebras;cyclic algebras;p-algebras;valuation theory;indecomposable division algebras