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Let A be a central simple algebra over a field F. Let k_1,\ldots, k_r becyclic 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 algebraswhere each k_i is in a symbol F-algebra factor of the same degree as k_i. As anapplication, we give an example of an indecomposable algebra of degree 8 andexponent 2 over a field of 2-cohomological dimension 4.

Power-Central Elements in Tensor Products of Symbol Algebras