Some remarks on u-S-Noetherian and u-S-coherent rings

2025/08/29 by Xiaolei Zhang, Wei Qi, Zhang, Xiaolei +1
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2508.21400

openalex publication_date 2025/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give some new characterizations of u-S-Noetherian rings and u-S-coherent rings in terms of uniform S-version of injective precovers, flat preenvelopes and absolutely pure modules, respectively. Moreover, we give a negative answer to a question proposed by Bouziri [3].

Citations

• On uniformly S-coherent rings
• Uniformly S-Noetherian rings
• On uniformly S-absolutely pure modules
• Characterizing S-projective modules and S-semisimple rings by uniformity
• Characterizing S-flat modules and S-von Neumann regular rings by uniformity

Related

• A note on S-flat preenvelopes
• A note on S-coherent rings
• On uniformly S-coherent rings
• New Characterizations of S-coherent rings
• Some new module-theoretic characterizations of S-coherent rings