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Hatcher-Topology-of-Numbers
· Problem 8.4.4
Quadratic Fields
Mathematics — Algebraic Topology · ideal-products
Problem
In
Z
[
−
5
]
\mathbb{Z}[\sqrt{-5}]
Z
[
−
5
]
compute
Q
2
Q^2
Q
2
for
Q
=
(
3
,
1
+
−
5
)
Q = (3, 1 + \sqrt{-5})
Q
=
(
3
,
1
+
−
5
)
as a principal ideal
(
α
)
(\alpha)
(
α
)
after first determining what
N
(
α
)
N(\alpha)
N
(
α
)
must be.
Related theory
Ideal And Non Ideal Solutions
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