Under a coprimeness condition on extension degrees, stable or retract rationality of norm one tori is preserved under tensor product, implying the Hasse norm principle holds for the combined extension over global fields.
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Rationality problem for norm one tori of tensor products of \'etale algebras and Hasse norm principle
Under a coprimeness condition on extension degrees, stable or retract rationality of norm one tori is preserved under tensor product, implying the Hasse norm principle holds for the combined extension over global fields.