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Kummer subfields of tame division algebras over Henselian fields
By generalizing the method used by Tignol and Amitsur in [J.-P. Tignol, S.A. Amitsur, Kummer subfields of Malcev–Neumann division algebras, Israel Journal of Math. 50 (1985), 114–144], we determine necessary and sufficient conditions for an arbitrary central division algebra D over a Henselian value...
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| Published in: | Journal of pure and applied algebra 2010-04, Vol.214 (4), p.440-448 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | By generalizing the method used by Tignol and Amitsur in [J.-P. Tignol, S.A. Amitsur, Kummer subfields of Malcev–Neumann division algebras, Israel Journal of Math. 50 (1985), 114–144], we determine necessary and sufficient conditions for an arbitrary central division algebra
D
over a Henselian valued field
E
to have Kummer subfields when the characteristic of the residue field
E
¯
of
E
does not divide the degree of
D
. We prove also that if
D
is a semiramified division algebra of degree
n
[resp., of prime power degree
p
r
] over
E
such that
char
(
E
¯
)
does not divide
n
and
rk
(
Γ
D
/
Γ
E
)
≥
3
[resp.,
p
≠
char
(
E
¯
)
and
p
3
divides
exp
(
Γ
D
/
Γ
E
)
], then
D
is non-cyclic [resp.,
D
is not an elementary abelian crossed product]. |
|---|---|
| ISSN: | 0022-4049 1873-1376 |
| DOI: | 10.1016/j.jpaa.2009.06.013 |