Theorems · Theorem · linear algebra

Submodule.map_iInf

∀ {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] {σ₁₂ : R →+* R₂}
  [inst_6 : RingHomSurjective σ₁₂] {ι : Sort u_9} [Nonempty ι] {p : ι → Submodule R M} (f : M →ₛₗ[σ₁₂] M₂),
  Function.Injective ⇑f → Submodule.map f (⨅ i, p i) = ⨅ i, Submodule.map f (p i)

Defined in

Mathlib.Algebra.Module.Submodule.Map

Cited by

2 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModuleRingHomSurjectiveNonempty