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Radical extensions and crossed homomorphisms

  • Fernando Barrera-Mora (a1) and Pablo Lam-Estrada (a1)

Abstract

If Ω/F is a Galois extension with Galois G and μ(Ω) denotes the group of roots of unity in Ω, we use the group Z1 (G,μ(Ω)) of crossed homomorphisms to study radical extensions inside Ω. Furthermore, we characterise cubic radical extension, and we provide an example to show that this result can not extended for higher degree extensions.

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References

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[1]Albu, T. and Nicolae, F., ‘Kneser field extensions with cogalois correspondence’, J. Number Theory 52 (1995), 299318.
[2]Barrera-Mora, F., ‘On Subfields of Radical Extensions’, Comm. Algebra 27 (1999), 46414649.
[3]Barrera-Mora, F., Rzedowski-Calderón, M. and Villa-Salvador, G., ‘On Cogalois extensions’, J. Pure Appl. Algebra 76 (1991), 111.
[4]Barrera-Mora, F. and Vélez, W.Y., ‘Some results on radical extensions’, J. Algebra 162 (1993), 295301.
[5]Isaacs, I.M. and Moulton, D.P., ‘Real fields and repeated radical extensions’, J. Algebra 201 (1998), 429455.
[6]Washington, L.C., Introduction to cyclotomic fields, Graduate Texts in Maths 83 (Springer-Verlag, New York, Berlin, Heidelberg, 1982).
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Radical extensions and crossed homomorphisms

  • Fernando Barrera-Mora (a1) and Pablo Lam-Estrada (a1)

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