Geodesic
Gradings of Galois extensions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2023) no. 4, pp. 11-29

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This paper is devoted to the gradings of finite field extensions in which all homogeneous components are one-dimensional. Such gradings are called fine. Kummer extensions are an important class of extensions that admit fine gradings. There always exists a standard grading of Kummer extension based on the Galois group. The paper describes all fine gradings of Kummer extensions, and, in particular, it establishes a criterion for any fine grading to be isomorphic to the standard one. We also investigate gradings of a wider class of Galois extensions that admit fine gradings. 
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     author = {D. A. Badulin and A. L. Kanunnikov},
     title = {Gradings of {Galois} extensions},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     publisher = {mathdoc},
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     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2023_24_4_a1/}
}
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D. A. Badulin; A. L. Kanunnikov. Gradings of Galois extensions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2023) no. 4, pp. 11-29. http://geodesic.mathdoc.fr/item/FPM_2023_24_4_a1/