Abstract
Let A be a central simple algebra over a field F. Let k1,…, kr be cyclic extensions of F such that k1 ⊗F… ⊗Fkr is a field. We investigate conditions under which A is a tensor product of symbol algebras where each field ki lies in a symbol F-algebra factor of the same degree as ki over F. 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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