Theorems · Theorem · number theory

QuadraticMap.Equivalent.rank_radical_eq

∀ {R : Type u_1} {M : Type u_2} {M' : Type u_3} {P : Type u_4} [inst : AddCommGroup M] [inst_1 : AddCommGroup M']
  [inst_2 : AddCommGroup P] [inst_3 : CommRing R] [inst_4 : Module R M] [inst_5 : Module R M'] [inst_6 : Module R P]
  {Q : QuadraticMap R M P} {Q' : QuadraticMap R M' P},
  Q.Equivalent Q' → Module.finrank R ↥Q.radical = Module.finrank R ↥Q'.radical

The rank of the radical of a quadratic map is invariant under equivalences.

Defined in

Mathlib.LinearAlgebra.QuadraticForm.Radical

Cited by

2 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddCommGroupAddCommGroupCommRingModuleModuleModule