JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (8): 75-80.doi: 10.6040/j.issn.1671-9352.0.2016.458

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Relative torsionless modules

XU Hui1,2, ZHAO Zhi-bing1*   

  1. 1. School of Mathematical Scicences, Anhui University, Hefei 230601, Anhui, China;
    2. Department of Basic Teaching, Anhui Business Vocational College, Hefei 231131, Anhui, China
  • Received:2016-09-22 Online:2017-08-20 Published:2017-08-03

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Abstract: Some elementary properties of relative torsionless modules with respect to a faithful and balanced bimodule are studied. Some equivalent conditions for a left or right Noether ring is a QF-ring is gotten. It is proved that a finitely generated module is an ω-torsionless module if and only if it is an ω-1-syzygy module if and only if it is an ω-1-torsionfree module when ω is a generalized tilting bimodule. Moreover, the extension closure of the class of ω-torsionless modules is investigated, and some classical results are generalized to the relative case.

Key words: extension closure, ω-torsionless modules, ω-reexive modules, (strong)grade of modules related to ω

CLC Number: 

  • O154.2
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