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Published online by Cambridge University Press: 29 June 2021
Let $\mathscr {A}$ be a topological Azumaya algebra of degree
$mn$ over a CW complex X. We give conditions for the positive integers m and n, and the space X so that
$\mathscr {A}$ can be decomposed as the tensor product of topological Azumaya algebras of degrees m and n. Then we prove that if
$m<n$ and the dimension of X is higher than
$2m+1$,
$\mathscr {A}$ may not have such decomposition.