最終更新日：2025/11/27
(number theory, field theory) A norm for the rational numbers, with some prime number p as parameter, such that any rational number of the form pᵏ(a/b) — where a, b and k are integers and a, b and p are coprime — is mapped to the rational number p⁻ᵏ and 0 is mapped to 0. (Note: any nonzero rational number can be reduced to such a form.)
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p-adic absolute value
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元となった辞書の項目
p-adic absolute value
名詞
(number
theory,
field
theory)
A
norm
for
the
rational
numbers,
with
some
prime
number
p
as
parameter,
such
that
any
rational
number
of
the
form
pᵏ(a/b)
—
where
a,
b
and
k
are
integers
and
a,
b
and
p
are
coprime
—
is
mapped
to
the
rational
number
p⁻ᵏ
and
0
is
mapped
to
0.
(Note:
any
nonzero
rational
number
can
be
reduced
to
such
a
form.)
日本語の意味
（数論、体論）ある素数 p をパラメータとして、有理数全体に定義されるノルム（絶対値関数）で、任意の非零有理数が p の冪乗因子に基づいた一意の形、すなわち pᵏ (a/b)（ここで a, b, k は整数で、a, b および p が互いに素である形）に表現でき、その値を p⁻ᵏ と定義し、0 は 0 と対応させるというものです。
意味（1）
(number
theory,
field
theory)
A
norm
for
the
rational
numbers,
with
some
prime
number
p
as
parameter,
such
that
any
rational
number
of
the
form
pᵏ(a/b)
—
where
a,
b
and
k
are
integers
and
a,
b
and
p
are
coprime
—
is
mapped
to
the
rational
number
p⁻ᵏ
and
0
is
mapped
to
0.
(Note:
any
nonzero
rational
number
can
be
reduced
to
such
a
form.)
（ plural ）
