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.
Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 254–260, February, 1999. |