JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (8): 94-98.doi: 10.6040/j.issn.1671-9352.0.2021.139

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Some notes on periodic modules

WANG Jian1, WU Jin-yong2   

  1. 1. College of Science, Jinling Institute of Technology, Nanjing 211169, Jiangsu, China;
    2. College of Mathematics and Physics, Wenzhou University, Wenzhou 325035, Zhejiang, China
  • Published:2021-08-09

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Abstract: Let R be a ring and A a class of left R-modules. Assume that A is a projectively resolving precovering class, using dimension shifting, a sufficient condition for an A -periodic left R-module M in A is obtained by applying the properties of A -dimensions and self-orthogonal modules. As an application, some characterizations of finiteness of the left global dimension of R are given which provided that the left Gorenstein global dimension of R is finite. In addition, under an extra condition, a characterization of infinitely presented partial tilting modules in A⊥ is supplied.

Key words: A -periodic module, left global dimension, partial tilting module

CLC Number: 

  • O154.2
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