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Legalese
About
the ramification index and the inertial degree are multiplicative in towers
(Theorem)
Theorem
1
Let
and
be
number fields
in a tower:
and let
and
be their
rings of integers
respectively. Suppose
is a
prime ideal
of
and let
be a prime ideal of
lying above
, and
is a prime ideal of
lying above
.
Then the
indices
of the
extensions
, the
ramification
indices and
inertial degrees
satisfy:
(
1
)
(
2
)
(
3
)
"the ramification index and the inertial degree are multiplicative in towers" is owned by
alozano
.
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See Also:
ramification index
,
inertial degree
Keywords:
towers of number fields, ramification, inertia
This object's
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Cross-references:
inertial degrees
,
ramification
,
extensions
,
indices
,
prime ideal
,
rings of integers
,
number fields
This is
version 2
of
the ramification index and the inertial degree are multiplicative in towers
, born on 2005-03-03, modified 2005-03-03.
Object id is
6842
, canonical name is
RamificationIndexAndTheInertialDegreeAreMultiplicativeInTowers
.
Accessed 1087 times total.
Classification:
AMS MSC
:
11S15
(Number theory :: Algebraic number theory: local and $p$-adic fields :: Ramification and extension theory)
13B02
(Commutative rings and algebras :: Ring extensions and related topics :: Extension theory)
12F99
(Field theory and polynomials :: Field extensions :: Miscellaneous)
Pending Errata and Addenda
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