A note on trinomial identities in associative algebras (Q1966194)

The author proves that the following are equivalent for an associative algebra \(A\) over an infinite field: \(A\) satisfies a trinomial identity (i.e., a polynomial identity with three or two non-zero terms); \(A\) satisfies a semigroup identity; \(A\) satisfies an identity of the form \(y^m[x,y,\ldots,y]y^k=0\); the variety generated by \(A\) does not contain the algebra of \(2\times 2\) upper triangular matrices. For related results see the paper [\textit{D. M. Riley, M. C. Wilson}, Glasg. Math. J. 41, No. 3, 453-462 (1999; see the preceding review Zbl 0954.16016)].