Geodesic
Construction of Auslander–Gorenstein local rings as Frobenius extensions
Mitsuo Hoshino1 ; Noritsugu Kameyama2 ; Hirotaka Koga3
1 Institute of Mathematics University of Tsukuba Tsukuba, Ibaraki, 305-8571, Japan
2 Interdisciplinary Graduate School of Science and Technology Shinshu University Nagano, 390-8621, Japan
3 School of Information Environment Tokyo Denki University Chiba, 270-1382, Japan
Colloquium Mathematicum, Tome 141 (2015) no. 1, pp. 1-11.

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Starting from an arbitrary ring $R$ we provide a systematic construction of $\mathbb {Z}/n\mathbb {Z}$-graded rings $A$ which are Frobenius extensions of $R$, and show that under mild assumptions, $A$ is an Auslander–Gorenstein local ring if and only if so is $R$.
DOI : 10.4064/cm141-1-1
Keywords: starting arbitrary ring provide systematic construction mathbb mathbb graded rings which frobenius extensions under mild assumptions nbsp auslander gorenstein local ring only

Mitsuo Hoshino 1 ; Noritsugu Kameyama 2 ; Hirotaka Koga 3

1 Institute of Mathematics University of Tsukuba Tsukuba, Ibaraki, 305-8571, Japan
2 Interdisciplinary Graduate School of Science and Technology Shinshu University Nagano, 390-8621, Japan
3 School of Information Environment Tokyo Denki University Chiba, 270-1382, Japan 
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Mitsuo Hoshino; Noritsugu Kameyama; Hirotaka Koga. Construction of Auslander–Gorenstein local
 rings as Frobenius extensions. Colloquium Mathematicum, Tome 141 (2015) no. 1, pp. 1-11. doi : 10.4064/cm141-1-1. http://geodesic.mathdoc.fr/articles/10.4064/cm141-1-1/

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