대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제60권4호
  • /
  • Pages.895-903
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  • 2023
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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SOME RESULTS ON 2-STRONGLY GORENSTEIN PROJECTIVE MODULES AND RELATED RINGS

  • Dong Chen (School of Electronic Information and Electrical Engineering Chengdu University) ;
  • Kui Hu (College of Science Southwest University of Science and Technology)
  • 투고 : 2022.06.07
  • 심사 : 2022.10.28
  • 발행 : 2023.07.31
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초록

In this paper, we give some results on 2-strongly Gorenstein projective modules and related rings. We first investigate the relationship between strongly Gorenstein projective modules and periodic modules and then give the structure of modules over strongly Gorenstein semisimple rings. Furthermore, we prove that a ring R is 2-strongly Gorenstein hereditary if and only if every ideal of R is Gorenstein projective and the class of 2-strongly Gorenstein projective modules is closed under extensions. Finally, we study the relationship between 2-Gorenstein projective hereditary and 2-Gorenstein projective semisimple rings, and we also give an example to show the quotient ring of a 2-Gorenstein projective hereditary ring is not necessarily 2-Gorenstein projective semisimple.

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과제정보

This work was financially supported by NSFC(11671283) and NSFC(11401493).

참고문헌

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