Right ideals generated by an idempotent of finite rank.
type: Item
instance of: scholarly article
title: Right ideals generated by an idempotent of finite rank.
zbMATH Open document ID: 1183.15015
author: Tsiu-Kwen Lee
author: Yiqiang Zhou
published in: Linear Algebra and its Applications
publication date: 2009-10-14T00:00:00Z
review text: Let \(R\) be a \(K\)-algebra acting densely on \(V(D)\). It is proved that a right ideal \(P\) of \(R\) is generated by an idempotent of finite rank if and only if the rank of \(f(x_1,\dots,x_t)\) is bounded above by the same natural number for all \(x_1,\dots,x_t\in P\). In this case, the rank of the idempotent that generates \(P\) is also explicitly given. The results are then applied to considering the triangularization of \(P\) and the irreducibility of \(f(P)\). Section 2 is proofs and consequences.
reviewed by: Yueh-er Kuo
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 16D25
Mathematics Subject Classification ID: 16R50
zbMATH DE Number: 5614889
zbMATH Keywords: irreducibility
zbMATH Keywords: triangularizations
zbMATH Keywords: right ideals
zbMATH Keywords: PI-algebras
zbMATH Keywords: ranks of idempotents
zbMATH Keywords: right vector spaces over division algebras
MaRDI profile type: Publication
full work available at URL: j.laa.2009.07.005
OpenAlex ID: W2048072141
Wikidata QID: Q57788007
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DOI: 10.1016/J.LAA.2009.07.005
description: scientific article; zbMATH DE number 5614889