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山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (11): 92-94.doi: 10.6040/j.issn.1671-9352.0.2017.008

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强余挠模的忠实平坦余基变换

王小青,梁力*   

  1. 兰州交通大学数理学院, 甘肃 兰州 730070
  • 收稿日期:2017-01-11 出版日期:2017-11-20 发布日期:2017-11-17
  • 通讯作者: 梁力(1980— ),男,博士,副教授,研究方向为同调代数. E-mail:lliang@mail.lzjtu.cn E-mail:wxq647982@163.com
  • 作者简介:王小青(1992— ),女,硕士研究生,研究方向为同调代数. E-mail:wxq647982@163.com
  • 基金资助:
    国家自然科学基金资助项目(11301240,11561039);甘肃省自然科学基金资助项目(1506RJZA075)

Strongly cotorsion modules under faithfully flat co-base change

WANG Xiao-qing, LIANG Li*   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Received:2017-01-11 Online:2017-11-20 Published:2017-11-17

摘要: 研究了强余挠模的忠实平坦余基变换。令R是环,S是忠实平坦R-代数,在一些额外的条件之下,证明了R-模G是强余挠的当且仅当HomR(S,G)是强余挠R-模且Ext>0R(S,G)=0;当且仅当HomR(S,G)是强余挠S-模且Ext>0R(S,G)=0。

关键词: 强余挠模, 忠实平坦余基变换, 余挠模

Abstract: Strongly cotorsion modules under faithfully flat co-base change are investigated. Let R be a commutative noetherian ring and S be a faithfully flat R-algebra. It is proved, under some extra assumptions, that an R-module G is strongly cotorsion if and only if HomR(S,G) is a strongly cotorsion R-module and Ext>0R(S,G)=0 if and only if HomR(S,G) is a strongly cotorsion S-module and Ext>0R(S,G)=0.

Key words: faithfully flat co-base change, strongly cotorsion module, cotorsion module

中图分类号: 

  • O154.2
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