Last Updated：2025/12/03
Sentence
整域から分数体を構成するには、各元を第二成分が0でない有序対 (a,b) の同値類として表し、加法を (a,b)+(a',b')=(ab'+a'b,bb')、乗法を成分ごとに定義する。
Quizzes for review
To construct the field of quotients from an integral domain, one represents each element as an equivalence class of ordered pairs (a,b) with b nonzero and defines addition by (a,b)+(a',b')=(ab'+a'b,bb') and multiplication coordinate-wise.
See correct answer
To construct the field of quotients from an integral domain, one represents each element as an equivalence class of ordered pairs (a,b) with b nonzero and defines addition by (a,b)+(a',b')=(ab'+a'b,bb') and multiplication coordinate-wise.
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Related words
field of quotients
Noun
(algebra)
A
field
all
of
whose
elements
can
be
represented
as
ordered
pairs
each
of
whose
components
belong
to
a
given
integral
domain,
such
that
the
second
component
is
non-zero,
and
so
that
the
additive
operator
is
defined
like
so:
(a,b)+(a',b')=(ab'+a'b,bb'),
the
multiplicative
operator
is
defined
coordinate-wise,
the
zero
is
(0,1),
the
unity
is
(1,1),
the
additive
inverse
of
(a,b)
is
(-a,b),
equivalence
is
defined
like
so:
(a,b)≡(a',b')
if
and
only
if
ab'=a'b,
and
multiplicative
inverse
of
a
non-zero–equivalent
element
(a,b)
is
(b,a).
Japanese Meaning
「field of quotients」とは、与えられた整域に対して、その各元を整域の非零元による順序対として表現し、加算および乗算が定義される体のことであり、分数体とも呼ばれます。
Related Words
English - English
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