대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제56권2호
  • /
  • Pages.373-382
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  • 2019
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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ON STRONGLY GORENSTEIN HEREDITARY RINGS

  • Hu, Kui (College of Science Southwest University of Science and Technology) ;
  • Kim, Hwankoo (Division of Computer and Information Engineering Hoseo University) ;
  • Wang, Fanggui (College of Mathematics and Software Science Sichuan Normal University) ;
  • Xu, Longyu (College of Science Southwest University of Science and Technology) ;
  • Zhou, Dechuan (College of Science Southwest University of Science and Technology)
  • 투고 : 2018.03.21
  • 심사 : 2018.09.07
  • 발행 : 2019.03.31
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초록

In this note, we mainly discuss strongly Gorenstein hereditary rings. We prove that for any ring, the class of SG-projective modules and the class of G-projective modules coincide if and only if the class of SG-projective modules is closed under extension. From this we get that a ring is an SG-hereditary ring if and only if every ideal is G-projective and the class of SG-projective modules is closed under extension. We also give some examples of domains whose ideals are SG-projective.

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참고문헌

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