In abstract algebra, Regev's theorem, proved by Amitai Regev (1971, 1972), states that the tensor product of two PI algebras is a PI algebra.
References
Regev, Amitai (1971), "Existence of polynomial identities in A⊗FB", Bulletin of the American Mathematical Society, 77 (6): 1067–1069, doi:10.1090/S0002-9904-1971-12869-0, ISSN 0002-9904, MR 0284468
Regev, Amitai (1972), "Existence of identities in A⊗B", Israel Journal of Mathematics, 11: 131–152, doi:10.1007/BF02762615, ISSN 0021-2172, MR 0314893
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