\(n\)-star modules over ring extensions.
type: Item
instance of: scholarly article
title: \(n\)-star modules over ring extensions.
zbMATH Open document ID: 1118.16011
author: Jiaqun Wei
published in: Journal of Algebra
publication date: 2007-04-16T00:00:00Z
review text: The author gives conditions under which an \(n\)-star module \(_AU\) extends to an \(n\)-star module, or an \(n\)-tilting module, \(_RR\otimes{_AU}\) over a ring extension \(R\) of \(A\). In case that \(R\) is a split extension of \(A\) by \(Q\), the author obtains that \(_RR\otimes{_AU}\) is a 1-tilting module (respectively, a 1-star module) iff \(_AU\) is a 1-tilting module (respectively, a 1-star module) and \(_AU\) generates both \(_AQ\otimes{_AU}\) and \(_A\Hom_A(Q,D)\) (respectively, \(_AU\) generates \(_AQ\otimes{_AU}\)), where \(_AD\) is an injective cogenerator in the category of all left \(A\)-modules. These extend results of \textit{I. Assem, N. Marmaridis} [Commun. Algebra 26, No. 5, 1547-1555 (1998; Zbl 0915.16007)], and \textit{K. R. Fuller} [Commun. Algebra 25, No. 9, 2839-2860 (1997; Zbl 0885.16019)] by removing the restrictions on \(R\) and \(Q\).
Mathematics Subject Classification ID: 16E30
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 5143569
zbMATH Keywords: star modules
zbMATH Keywords: tilting modules
zbMATH Keywords: ring extensions
zbMATH Keywords: injective cogenerators
zbMATH Keywords: categories of left modules
reviewed by: Tong Wenting
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.10.026
OpenAlex ID: W2083476358
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DOI: 10.1016/J.JALGEBRA.2006.10.026
description: scientific article; zbMATH DE number 5143569