Documentation
Mathlib
.
RingTheory
.
ZMod
.
Torsion
Search
return to top
source
Imports
Init
Mathlib.FieldTheory.Finite.Basic
Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity
Imported by
ZMod
.
rootsOfUnity_eq_top
ZMod
.
instHasEnoughRootsOfUnityHSubNatOfNat
Torsion group of
ZMod
p
for prime
p
#
This file shows that the
ZMod
p
has
p - 1
roots-of-unity.
source
theorem
ZMod
.
rootsOfUnity_eq_top
{
p
:
ℕ
}
[
Fact
(
Nat.Prime
p
)
]
:
rootsOfUnity
(
p
-
1
)
(
ZMod
p
)
=
⊤
source
instance
ZMod
.
instHasEnoughRootsOfUnityHSubNatOfNat
{
p
:
ℕ
}
[
Fact
(
Nat.Prime
p
)
]
:
HasEnoughRootsOfUnity
(
ZMod
p
)
(
p
-
1
)