Bull. Korean Math. Soc.
Published online July 1, 2022
Copyright © The Korean Mathematical Society.
Kui Hu, Hwankoo Kim, and Dechuan Zhou
Southwest University of Science and Technology, Hoseo University
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 $n$.
Keywords: Artinian local ring; QF-ring; G-semisimple ring; SG-semisimple ring; 2-SG-semisimple ring.
MSC numbers: 13G05; 13D03
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