Theorems · Theorem · group theory

LinearEquiv.finrank_quotient_sup_span_singleton

∀ {K : Type u_1} [inst : DivisionRing K] {V : Type u_2} [inst_1 : AddCommGroup V] [inst_2 : Module K V]
  [Module.Finite K V] {W : Submodule K V} {v : V},
  v ∉ W → Module.finrank K (V ⧸ W ⊔ K ∙ v) + 1 = Module.finrank K (V ⧸ W)

Defined in: Mathlib.LinearAlgebra.Transvection.Generation
Cited by: 1 results in Mathlib
Foundations: Depth 119 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
AddCommGroupstatement and proof · cited by 12,871
Submodulestatement and proof · cited by 7,192
HasQuotient.Quotientstatement and proof · cited by 2,301
Module.finrankstatement and proof · cited by 1,770
Submodule.spanstatement and proof · cited by 1,504
DivisionRingstatement and proof · cited by 1,062
Module.Finitestatement and proof · cited by 1,032
Submodule.finrank_quotient_add_finrankproof · cited by 13
Submodule.finrank_sup_span_singletonproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

LinearEquiv.mem_transvections_pow_mul_dilatransvections_of_fixedReduce_ne_smul_idproof · cited by 1