Identities of the algebra of triangular matrices

A. Sh. Abakarov

Zapiski Nauchnykh Seminarov POMI, Modules and algebraic groups, Tome 114 (1982), pp. 7-27

Résumé

This paper deals with the ideals of identities of certain associative algebras over a field $F$ of characteristic zero. An algebra $W$ of matrices of the form$\begin{pmatrix} \lambda & \mu \\ 0 & \omega \end{pmatrix}$, $\lambda\in\Lambda$, $\omega\in\Omega$, $\mu\in M$, where $\Lambda$ and $\Omega$, are $F$-algebras with unity and $M$ is a $(\Lambda,\Omega)$-bimodule, is considered. Under certain natural restrictions on $M$ one obtains the equality of ideals of identities $T(W)=T(\Lambda)T(\Omega)$, if $[[x_1,x_2],x_3[x_4,x_5]]\in T(\Omega)$.