Trace identities of the algebra of triangular matrices. (Russian) Zbl 0654.16013

Vajs, A. Ya.

Sib. Mat. Zh. 29, No. 3(169), 26-34 (1988).

Let \(T_ n(K)\) be the algebra of upper triangular \(n\times n\) matrices over a field K. The author proves that the ideal of trace identities of \(T_ n(K)\) is finitely generated, so that every trace identity of \(T_ n(K)\) is a consequence of certain basic trace identities \(f_ 1,f_ 2,...,f_ m\). The author computes the identities \(f_ 1,...,f_ m\).

Reviewer: Yu.N.Mal’tsev

MSC:

16Rxx	Rings with polynomial identity
16S50	Endomorphism rings; matrix rings

Keywords:

algebra of upper triangular n\(\times n\) matrices; ideal of trace identities