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RingTheory
.
SimpleModule
.
Rank
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Imports
Init
Mathlib.LinearAlgebra.FiniteDimensional
Mathlib.RingTheory.SimpleModule.Basic
Imported by
isSimpleModule_iff_finrank_eq_one
A module over a division ring is simple iff it has rank one
#
source
theorem
isSimpleModule_iff_finrank_eq_one
{R :
Type
u_1}
{M :
Type
u_2}
[
DivisionRing
R
]
[
AddCommGroup
M
]
[
Module
R
M
]
:
IsSimpleModule
R
M
↔
Module.finrank
R
M
=
1