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Galois module
In
mathematics
, a
Galois module
is a
G-module
, with
G
being the
Galois group
of some
extension
of
fields
. The term
Galois representation
is frequently used when the
G
-module is a
vector space
over a
field
or a
free module
over a
ring
, but can also be used as a synonym for
G
-module. The study of Galois modules for extensions of
local
or
global fields
is an important tool in
number theory
.
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