Power-Central Elements in Tensor Products of Symbol Algebras

Demba Barry (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Mots clés: Central simple algebra; Symbol algebra; Armature; Valuation; Cohomological dimension

Domaines: Anneaux et algèbres [math.RA]

Demba Barry. Power-Central Elements in Tensor Products of Symbol Algebras. 2013. ⟨hal-00875041⟩