强Prüfer环的同调刻画

王芳贵, 乔磊, 周德川

数学学报 ›› 2021, Vol. 64 ›› Issue (2) : 311-316.

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数学学报 ›› 2021, Vol. 64 ›› Issue (2) : 311-316. DOI: 10.12386/A2021sxxb0028
论文

强Prüfer环的同调刻画

    王芳贵1, 乔磊1, 周德川2
作者信息 +

A Homological Characterization of Strong Prüfer Rings

    Fang Gui WANG1, Lei QIAO1, De Chuan ZHOU2
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摘要

R是环,R的小finitistic维数定义为fPD (R)=sup{pdRM|M∈FBR}.本文证明了:若R是连通的强Prüfer环,则fPD (R ≤ 1.也证明了若R是强Prüfer环,M∈FBR,且MQ-挠模,则pdRM ≤ 1.

Abstract

Let R be a commutative ring. Then the small finitistic projective dimension of R is defined as fPD(R)=sup{pdRM|M ∈ FPR}. In this paper, it is shown that if R is a connected strong Prüfer ring, then fPD(R) ≤ 1. It is also shown that if R is a strong Prüfer ring, and if M is a Q-torsion module with M ∈ FPR, then pdRM ≤ 1.

关键词

有限投射分解 / 小finitistic维数 / Q-挠模 / 强Prü / fer环 / 连通环

Key words

finite projective resolution / small finitistic projective dimension / Q-torison module / strong Prü / fer ring / connected ring

引用本文

导出引用
王芳贵, 乔磊, 周德川. 强Prüfer环的同调刻画. 数学学报, 2021, 64(2): 311-316 https://doi.org/10.12386/A2021sxxb0028
Fang Gui WANG, Lei QIAO, De Chuan ZHOU. A Homological Characterization of Strong Prüfer Rings. Acta Mathematica Sinica, Chinese Series, 2021, 64(2): 311-316 https://doi.org/10.12386/A2021sxxb0028

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基金

国家自然科学基金资助项目(11671283,11701398)

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