Train algebras of rank 3 with finiteness conditions
type: Item
instance of: scholarly article
title: Train algebras of rank 3 with finiteness conditions
zbMATH Open document ID: 1206.17023
author: Fouad Zitan
published in: Linear Algebra and its Applications
publication date: 2009-07-02T00:00:00Z
review text: A train algebra of rank \(r\) is a commutative baric algebra \((A,\omega)\) satisfying the so-called train equation of \(A\): \[ x^r+\gamma_1\omega(x)x^{r-1}+\cdots+\gamma_{r1}\omega(x)^{r-1}x=0. \] This paper deals with train algebras of rank 3. In particular, it is proved that any Noetherian (or Artinian or finitely generated) train algebra of rank 3 is finitely dimensional.
Mathematics Subject Classification ID: 17D92
Mathematics Subject Classification ID: 17A30
zbMATH DE Number: 5574588
zbMATH Keywords: Train algebra
zbMATH Keywords: finitely generated algebra
zbMATH Keywords: Noetherian algebra
zbMATH Keywords: Artinian algebra
zbMATH Keywords: finiteness conditions
reviewed by: Antonio M. Oller Marcén
MaRDI profile type: Publication
full work available at URL: j.laa.2009.04.006
OpenAlex ID: W2128421829
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DOI: 10.1016/J.LAA.2009.04.006
description: scientific article; zbMATH DE number 5574588