Research Article

Uniformly S-Noetherian rings

Published in: Quaestiones Mathematicae
Volume 47 , issue 5 , 2024 , pages: 1019–1038

DOI: 10.2989/16073606.2023.2278744

Author(s): Mingzhao Chen Leshan Normal University, China , Hwankoo Kim Hoseo University, Republic of Korea , Wei Qi Shandong University of Technology, China , Fanggui Wang Sichuan Normal University, China , Wei Zhao ABa Teachers University, China

Keywords: 13E05 , 13A15 , 13C11 , 13D30 , Uniformly S-Noetherian ring , uniformly S-Noetherian module , u-S-injective module , trivial extension , pullback , amalgamated algebra

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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-Nagata-Formanek theorem for uniformly S-Noetherian rings. In addition, the uniformly S-Noetherian properties on several ring constructions are given. The notion of u-S-injective modules is also introduced and studied. Finally, we obtain the Bass-Papp theorem for uniformly S-Noetherian rings.

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