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 and be commutative rings with unity, a ring homomorphism and an ideal of . Then the subring and of is called the amalgamation of with along with respect to . In this paper, we determine when is a (generalized) filter ring.
Various results on the induced representations of group rings are extended to modules over strongly group-graded rings. In particular, a proof of the graded version of Mackey's theorem is given.