Functional identities on tensor products of algebras

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Functional identities on tensor products of algebras

Brešar, Matej

Journal of algebra, 06/2016, Volume: 455

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Let R and S be unital algebras. We show that if X is a d-free subset of R and S is finite dimensional, then the set X={x⊗s|x∈X,s∈S} is a d-free subset of the algebra R⊗S. The assumption that S is finite dimensional turns out to be necessary in general. However, we show that some important functional identities have only standard solutions on X even when S is infinite dimensional.

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Brešar, Matej

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