Uniformly S-Noetherian rings

Abstract

Let R be a ring and S be a multiplicative subset of R. Then R is called a uniformly S-Noetherian ring if there exists s ∈ S such that, for any  ideal I of R, sI ⊆ K for some finitely generated subideal K of I. We give the Eakin-NagataFormanek theorem for uniformly S-Noetherian  rings. In addition, the uniformly S-Noetherian properties on several ring constructions are given. The notion of u-Sinjective modules is  also introduced and studied. Finally, we obtain the Bass-Papp theorem for uniformly S-Noetherian rings.