Power-Central Elements in Tensor Products of Symbol Algebras.

LetAbe a central simple algebra over a fieldF. Letk1,…,krbe cyclic extensions ofFsuch thatk1 ⊗F… ⊗Fkris a field. We investigate conditions under whichAis a tensor product of symbol algebras where each fieldkilies in a symbolF-algebra factor of the same degree askioverF. 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. [ABSTRACT FROM PUBLISHER]