On the multiplication ideal of a nonassociative algebra
type: Item
instance of: scholarly article
title: On the multiplication ideal of a nonassociative algebra
zbMATH Open document ID: 0594.17003
DOI: 10.1007/BF01195102
author: Scott M. Farrand
author: David R. Finston
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: The composition factors of a finite dimensional algebra, viewed as a left module for its multiplication algebra, correspond to the simple algebras in the Wedderburn-Artin decomposition of the multiplication algebra modulo its Jacobson radical. If the algebra has no nilpotent elements and the base field is algebraically closed, the correspondence is one-to-one. We conclude, for nilpotent free algebras, that the multiplication algebra and multiplication ideal coincide and the centroid is a commutative subalgebra of the multiplication algebra.
Mathematics Subject Classification ID: 17A60
Mathematics Subject Classification ID: 17A65
zbMATH DE Number: 3955159
zbMATH Keywords: nilpotent free algebras
zbMATH Keywords: multiplication algebra
zbMATH Keywords: multiplication ideal
MaRDI profile type: Publication
cites work: Q5777227
cites work: A theorem on non-associative algebras and its application to differential equations
cites work: Nicht assoziative separable Algebren über Ringen
description: scientific article; zbMATH DE number 3955159