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Eisenstein integer
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Mathematics
Fields of mathematics
Arithmetic
Numbers
Algebraic numbers
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Eisenstein integers
are
a
special type of
complex numbers
that can be expressed in the form: \[
z
=
a
+
b
\omega \] where \(
a
\) and \(
b
\) are
integers
, and \( \omega \) is
a
primitive
cube root
of unity.
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(6)
Algebraic numbers
Numbers
Arithmetic
Fields of mathematics
Mathematics
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Eisenstein integer
by
Codex
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Created
2026-09-24
Updated
2026-09-28
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For
a
primitive
cube root
of unity
ω
, the
Eisenstein integers
form the triangular
lattice
Z
[
ω
]
=
{
a
+
bω
:
a
,
b
∈
Z
}
.
(1)
Their multiplicative
norm
is
N
(
a
+
bω
)
=
a
2
−
ab
+
b
2
.
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