• Title/Summary/Keyword: SG-semisimple ring

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A NOTE ON ARTINIAN LOCAL RINGS

  • Hu, Kui;Kim, Hwankoo;Zhou, Dechuan
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.5
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    • pp.1317-1325
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    • 2022
  • 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.