最終更新日：2025/12/05
(algebra) A ring whose elements are fractions whose numerators belong to a given commutative unital ring and whose denominators belong to a multiplicatively closed unital subset D of that given ring. Addition and multiplication of such fractions is defined just as for a field of fractions. A pair of fractions a/b and c/d are deemed equivalent if there is a member x of D such that x(ad-bc)=0.
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ring of fractions
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元となった辞書の項目
ring of fractions
名詞
(algebra)
A
ring
whose
elements
are
fractions
whose
numerators
belong
to
a
given
commutative
unital
ring
and
whose
denominators
belong
to
a
multiplicatively
closed
unital
subset
D
of
that
given
ring.
Addition
and
multiplication
of
such
fractions
is
defined
just
as
for
a
field
of
fractions.
A
pair
of
fractions
a/b
and
c/d
are
deemed
equivalent
if
there
is
a
member
x
of
D
such
that
x(ad-bc)=0.
日本語の意味
(代数学) ある可換単位元付き環と、その環内の乗法的に閉じた単位集合Dに対して、分子がその環の元、分母がDの元である分数たちを要素とする環。これらの分数の加法および乗法は、分数体の場合と同様に定義され、例えばa/bとc/dは、Dの元xが存在してx(ad - bc) = 0となるときに同値とみなされる。
意味（1）
(algebra)
A
ring
whose
elements
are
fractions
whose
numerators
belong
to
a
given
commutative
unital
ring
and
whose
denominators
belong
to
a
multiplicatively
closed
unital
subset
D
of
that
given
ring.
Addition
and
multiplication
of
such
fractions
is
defined
just
as
for
a
field
of
fractions.
A
pair
of
fractions
a/b
and
c/d
are
deemed
equivalent
if
there
is
a
member
x
of
D
such
that
x(ad-bc)=0.
（ plural ）
