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A note on Artinian local rings

김환구|Kui Hu|De Chuan Zhou
대한수학회 (The Korean Mathematical Society)|2022.09|대한수학회보 (Bulletin of the KMS)|제59권 제5호|pp. 1317-1325|DOI 10.4134/BKMS.b210759

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키워드

Artinian local ringQF-ringG-semisimple ringSG-semisimple ring$2$-SG-semisimple ring
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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 $n$.

Abstract

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 $n$.

참고문헌 (20)

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