Power-Central Elements in Tensor Products of Symbol Algebras

2013/10/21 by Demba Barry, Barry, Demba
Mathematics · #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.1310.5423

20 pages

arxiv created 2013/10/21 · arxiv updated 2013/10/22

Abstract

Let A be a central simple algebra over a field F. Let k₁,…, k_r be cyclic extensions of F such that k₁⊗_F⋯ ⊗_F k_r is a field. We investigate conditions under which A is a tensor product of symbol algebras where each k_i is in a symbol F-algebra factor of the same degree as k_i. As an application, we give an example of an indecomposable algebra of degree 8 and exponent 2 over a field of 2-cohomological dimension 4.

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