Bulletin of the
Korean Mathematical Society BKMS

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