Genus fields of Kummer ℓn-cyclic extensions
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We give a construction of the genus field for Kummer [Formula: see text]-cyclic extensions of rational congruence function fields, where [Formula: see text] is a prime number. First, we compute the genus field of a field contained in a cyclotomic function field, and then for the general case. This generalizes the result obtained by Peng for a Kummer [Formula: see text]-cyclic extension. Finally, we study the extension [Formula: see text], for [Formula: see text], [Formula: see text] abelian extensions of [Formula: see text].
2013 ◽
Vol 09
(05)
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pp. 1249-1262
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2014 ◽
Vol 150
(4)
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pp. 507-522
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2020 ◽
Vol 0
(0)
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1959 ◽
Vol 14
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pp. 223-234
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2010 ◽
Vol 88
(3)
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pp. 301-312
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2010 ◽
Vol 130
(4)
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pp. 1048-1055
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1995 ◽
Vol 38
(2)
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pp. 167-173
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2020 ◽
Vol 16
(09)
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pp. 2041-2094
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