\(n\)-star modules over ring extensions.
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 \(Q\).
scientific article; zbMATH DE number 5143569
scientific article