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A Note on Co-Harada Rings

Abstract

In the early 1990s, Harada and Oshiro introduced extending and lifting properties for modules and, simultaneously, considered two new classes of artinian rings which contain quasi-Frobenius (QF-) rings and Nakayama rings: one is the class of right Harada rings and the other is the class of right co-Harada rings. Although QF-rings and Nakayama rings are left-right symmetric, Harada and co-Harada rings are not left-right symmetric. However, Oshiro showed that left Harada rings and right co-Harada rings are coinside. In this paper we provide many characterizations of right co-Harada rings and (right and left) co-Harada rings.

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2018.02.

The authors would like to thank the referees for their useful suggestions.

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Correspondence to Banh Duc Dung.

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Dan, P., Dung, B.D. A Note on Co-Harada Rings. Vietnam J. Math. 50, 161–169 (2022). https://doi.org/10.1007/s10013-021-00481-z

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  • DOI: https://doi.org/10.1007/s10013-021-00481-z

Keywords

  • Harada rings
  • Co-Harada rings
  • Small modules
  • Nonsmall modules
  • Cosmall modules
  • Non-cosmall modules

Mathematics Subject Classification (2010)

  • 16D70
  • 16D80
  • 16P20