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A NOTE ON ARTINIAN LOCAL RINGS

  • Hu, Kui (College of Science Southwest University of Science and Technology) ;
  • Kim, Hwankoo (Division of Computer Engineering Hoseo University) ;
  • Zhou, Dechuan (College of Science Southwest University of Science and Technology)
  • 투고 : 2021.10.17
  • 심사 : 2022.02.23
  • 발행 : 2022.09.30

초록

In this note, we prove that an Artinian local ring is G-semisimple (resp., SG-semisimple, 2-SG-semisimple) if and only if its maximal ideal is G-projective (resp., SG-projective, 2-SG-projective). As a corollary, we obtain the global statement of the above. We also give some examples of local G-semisimple rings whose maximal ideals are n-generated for some positive integer n.

키워드

과제정보

The authors would like to express their sincere thanks for the reviewer for his/her careful reading and an interesting suggestion.

참고문헌

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