JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (10): 52-58.doi: 10.6040/j.issn.1671-9352.0.2021.623

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Torsionfreeness and reflexivity under Frobenius extensions

ZHOU Rui, ZHAO Zhi-bing*   

  1. School of Mathematical Sciences, Anhui University, Hefei 230601, Anhui, China
  • Published:2022-10-06

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Abstract: Let A/R be a Frobenius extension of rings, we prove that torsionfreeness and reflexivity of modules are preserved under Frobenius extension, that is, for an A-module M, MA is torsionfree(resp. reflexive)as an A-module if and only if M is torsionfree(resp. reexive)as an R-module.

Key words: torsionfree modules, reflexive modules, Forbenius extensions

CLC Number: 

  • O154.2
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