Last Updated：2025/11/20
(algebra, number theory) A real or complex number (more generally, an element of a number field) which is a root of a monic polynomial whose coefficients are integers; equivalently, an algebraic number whose minimal polynomial (lowest-degree polynomial of which it is a root and whose leading coefficient is 1) has integer coefficients.
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algebraic integer
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Source Word
algebraic integer
Noun
(algebra,
number
theory)
A
real
or
complex
number
(more
generally,
an
element
of
a
number
field)
which
is
a
root
of
a
monic
polynomial
whose
coefficients
are
integers;
equivalently,
an
algebraic
number
whose
minimal
polynomial
(lowest-degree
polynomial
of
which
it
is
a
root
and
whose
leading
coefficient
is
1)
has
integer
coefficients.
Japanese Meaning
整数係数の首項が1である単項多項式の根となる実数または複素数。 / より一般には、最小多項式（その数を根に持つ係数が1の最低次数の多項式）が整数係数である代数数。
Sense（1）
(algebra,
number
theory)
A
real
or
complex
number
(more
generally,
an
element
of
a
number
field)
which
is
a
root
of
a
monic
polynomial
whose
coefficients
are
integers;
equivalently,
an
algebraic
number
whose
minimal
polynomial
(lowest-degree
polynomial
of
which
it
is
a
root
and
whose
leading
coefficient
is
1)
has
integer
coefficients.
（ plural ）
