Theorems · Theorem · linear algebra

Submodule.map_symm_eq_iff

∀ {R : Type u_1} {R₂ : Type u_3} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {τ₁₂ : R →+* R₂}
  {τ₂₁ : R₂ →+* R} [inst_6 : RingHomInvPair τ₁₂ τ₂₁] [inst_7 : RingHomInvPair τ₂₁ τ₁₂] {p : Submodule R M}
  (e : M ≃ₛₗ[τ₁₂] M₂) {K : Submodule R₂ M₂}, Submodule.map (↑e.symm) K = p ↔ Submodule.map (↑e) p = K

Defined in

Mathlib.Algebra.Module.Submodule.Map

Cited by

3 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModuleRingHomInvPairRingHomInvPair