Abstract
In the paper, trinomial identities of associative algebras over an infinite field are considered (in general, the algebras may have no unit), i.e., identities of the formα m 1+β m 2+γ m 3=0, where α, β, and γ are scalars andm 1,m 2, andm 3 are different monomials. It is shown that any nontrivial identity if this kind implies a semigroup identity. The algebras with trinomial identities are characterized in the language of varieties.
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References
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Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 254–260, February, 1999.
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Samoilov, L.M. A note on trinomial identities in associative algebras. Math Notes 65, 208–213 (1999). https://doi.org/10.1007/BF02679818
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DOI: https://doi.org/10.1007/BF02679818