On τ_q-flatness and τ_q-coherence

2021/11/05 by Xiaolei Zhang, Zhang, Xiaolei, Qi, Wei
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2111.03417

openalex publication_date 2021/11/05 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce and study the notions of τ_q-flat modules and τ_q-coheret rings. First, by investigating the Nagata rings of τ_q-torsion theory, we show that the small finitistic dimensions of T(R[x]) are all equal to 0 for any ring R. Then, we introduce the notion of τ_q-VN regular rings (i.e. over which all modules are τ_q-flat), and show that a ring R is a τ_q-VN regular ring if and only if T(R[x]) is a von Neumann regular ring. Finally, we obtain the Chase theorem for τ_q-coheret rings: a ring R is τ_q-coherent if and only if any direct product of R is τ_q-flat if and only if any direct product of flat R-modules is τ_q-flat. Some examples are provided to compare with the known conceptions.

Citations

• Two generalizations of projective modules and their applications
• On w-modules over strong mori domains

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