Demba Barry: Power-Central Elements in Tensor Products of Symbol Algebras

barry.demba@gmail.com

Submission: 2013, Oct 20

Let A be a central simple algebra over a field F. Let k_1,\ldots, k_r be cyclic extensions of F such that k_1\otimes_F\cdots \otimes_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.

2010 Mathematics Subject Classification: 16K20, 16W60, 12E15, 12G10, 16K50.

Keywords and Phrases: Central simple algebra, Symbol algebra, Armature, Valuation, Cohomological dimension.

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