Triangular representations of nilpotent graded associative algebras (Q1112930)

The theory of representations of graded associative algebras of the form \(R_ 1\oplus...\oplus R_ n\) over an arbitrary commutative ring is studied. Sufficient conditions, that an algebra of this form is a T- algebra for a given triangular configuration T (this means, that T is a transitive relation on \({\mathbb{N}}\) consisting of pairs (i,j), where \(i\leq j\) and 0 elsewhere), are found. As a corollary the well-known result of Bergman, that any algebra of such form can be embedded in an algebra of strictly upper triangular matrices of order \(n+1\) over some commutative algebra, is derived.