| 强Prüfer环的同调刻画 |
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| 引用本文： | 王芳贵,乔磊,周德川.强Prüfer环的同调刻画[J].数学学报,2021(2):311-316. |
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| 作者姓名： | 王芳贵 乔磊 周德川 |
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| 作者单位： | 四川师范大学数学科学学院;西南科技大学理学院 |
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| 基金项目： | 国家自然科学基金资助项目(11671283,11701398)。 |
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| 摘 要： | 设R是环,R的小finitistic维数定义为fPD(R)=sup{pdRM|M∈FPR}.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Prufer环,M∈FPR,且M是Q-挠模,则pdRM≤1.
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| 关 键 词： | 有限投射分解 小finitistic维数 Q-挠模 强Prüfer环 连通环 |
A Homological Characterization of Strong Prüfer Rings |
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| Fang Gui WANG,Lei QIAO,De Chuan ZHOU.A Homological Characterization of Strong Prüfer Rings[J].Acta Mathematica Sinica,2021(2):311-316. |
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| Authors: | Fang Gui WANG Lei QIAO De Chuan ZHOU |
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| Institution: | (School of Mathematical Sciences,Sichuan Normal University,Chengdu 610068,P.R.China;College of Science,Southwest University of Science and Technology,Mianyang 621010,P.R.China) |
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| 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. |
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| Keywords: | finite projective resolution small finitistic projective dimension Q-torison module strong Prüfer ring connected ring |
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