最終更新日：2024/08/05
(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).
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field of quotients
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元となった辞書の項目
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).
意味（1）
(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).
