Verification of non-identities in algebras
We present a computer assisted algorithm which establishes whether or not a proposed identity is a consequence of the defining identities of a variety of nonassociative algebras. When the nonassociative polynomial is not an identity, the algorithm produces a proof called a characteristic function. Like an ordinary counterexample, the characteristic function can be used to convince a verifier that the polynomial is not identically zero. However the characteristic function appears to be computationally easier to verify. Also, it reduces or eliminates problems with characteristic. We used this method to obtain and verify a new result in the theory of nonassociative algebras. Namely, in a free right alternative algebra (a,a,b)3≠0.
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