Theorems · Theorem · group theory

LinearEquiv.finrank_le_one_add_finrank_fixedSubmodule_dilatransvection

∀ {K : Type u_1} [inst : DivisionRing K] {V : Type u_2} [inst_1 : AddCommGroup V] [inst_2 : Module K V]
  [Module.Finite K V],
  ∀ e ∈ LinearEquiv.dilatransvections K V, Module.finrank K V ≤ 1 + Module.finrank K ↥(↑e).fixedSubmodule

Defined in: Mathlib.LinearAlgebra.Transvection.Generation
Cited by: 2 results in Mathlib
Foundations: Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DivisionRing AddCommGroup Module Module.Finite

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
AddCommGroupstatement and proof · cited by 12,871
Submodulestatement and proof · cited by 7,192
LinearEquivstatement and proof · cited by 3,317
Module.finrankstatement and proof · cited by 1,770
add_commproof · cited by 1,535
LinearEquiv.toLinearMapstatement and proof · cited by 1,171
DivisionRingstatement and proof · cited by 1,062
Module.Finitestatement and proof · cited by 1,032
LinearMap.rangeproof · cited by 893

Cited by2

Results whose statement or proof uses this declaration.

LinearEquiv.le_one_add_finrank_fixedSubmodule_dilatransvection_mulproof · cited by 1
LinearEquiv.le_one_add_finrank_fixedSubmodule_mul_dilatransvectionproof · cited by 1