Triangular representations of nilpotent graded associative algebras
type: Item
instance of: scholarly article
title: Triangular representations of nilpotent graded associative algebras
zbMATH Open document ID: 0661.16018
DOI: 10.1007/BF00975020
author: N. G. Nesterenko
published in: Siberian Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 4079667
zbMATH Keywords: representations of graded associative algebras
zbMATH Keywords: T-algebra
zbMATH Keywords: triangular configuration
zbMATH Keywords: embedded in an algebra of strictly upper triangular matrices
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00975020
OpenAlex ID: W2090392051
description: scientific article; zbMATH DE number 4079667