Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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HOMOLOGICAL PROPERTIES OF SEMI-WAKAMATSU-TILTING MODULES

  • Liu, Dajun (Institute of Mathematics School of Mathematics Sciences Nanjing Normal University) ;
  • Wei, Jiaqun (Institute of Mathematics School of Mathematics Sciences Nanjing Normal University)
  • Received : 2019.05.27
  • Accepted : 2020.01.17
  • Published : 2020.05.31
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Abstract

For a fixed semi-Wakamatsu-tilting module AT, we generalize the concepts of Auslander class, Bass class, and investigate many homological properties of such classes. Moreover, we establish an equivalence between the class of ∞-T-cotorsionfree modules and a subclass of the class of T-adstatic modules. Finally, a similar version of Auslander-Bridger approximation theorem and a nice property of relative cotranspose are obtained.

Keywords

Acknowledgement

This work was financially supported by the National Science Foundation of China (Grant No. 11771212) and the National Science Foundation for Distinguished Young Scholars of Jiangsu Province (Grant No. BK2012044) and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. The authors would like to thank the referee for helpful comments and suggestions on the last version of the paper.

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