Theorems · Theorem · linear algebra

LinearEquiv.ker

∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] {module_M : Module R M} {module_M₂ : Module R₂ M₂}
  {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} {re₁₂ : RingHomInvPair σ₁₂ σ₂₁} {re₂₁ : RingHomInvPair σ₂₁ σ₁₂} (e : M ≃ₛₗ[σ₁₂] M₂),
  (↑e).ker = ⊥

Defined in

Mathlib.Algebra.Module.Submodule.Ker

Cited by

16 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoid