General symbols and presentations of elementary linear groups.
Let be a commutative ring and a multiplicative system of ideals. We say that is -Noetherian, if for each ideal of , there exist and a finitely generated ideal such that . In this paper, we study the transfer of this property to the polynomial ring and Nagata’s idealization.
Let be a ring extension of . We show the left -module with the endmorphism ring End is a generalized tilting module when is a generalized tilting module under some conditions.