JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (4): 72-79.doi: 10.6040/j.issn.1671-9352.0.2018.105

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On homological properties of C-torsionless and C-reflexive modules

LUO Xiao-qiang1, TAN Ling-ling2*, XING Jian-min3   

  1. 1. Department of Mathematics, Sichuan University of Arts and Science, Dazhou 635000, Sichuan, China;
    2. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China;
    3. School of Mathematic and Physics, Qingdao University of Science and Technology, Qingdao 266061, Shandong, China
  • Published:2019-04-08

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Abstract: The relative notions and homological properties of torsionless and reflexive modules with respect to a semidualizing module are investigated. If C is a 1-dualizing module, then each submodule of a projective module is totally C-reflexive, and then the characterizations of C-torsionless and C-reflexive modules with finite GC-dimension are investigated. Moreover, the relations between the GC-dimension and the left C-orthogonal dimension of a module are studied, and some sufficient conditionson the existence of C-reflexive envelope are given.

Key words: C-torsionless module, C-reflexive module, totally C-reflexive module, semidualizing module, C-reflexive envelope

CLC Number: 

  • O154.2
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