Theorems · Theorem · commutative algebra

IsLocalizedModule.of_exists_mul_mem

∀ {R : Type u_1} [inst : CommSemiring R] {M : Type u_2} [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {N : Type u_6}
  [inst_3 : AddCommMonoid N] [inst_4 : Module R N] (S T : Submonoid R),
  S ≤ T → (∀ (x : ↥T), ∃ m, m * ↑x ∈ S) → ∀ (f : M →ₗ[R] N) [IsLocalizedModule S f], IsLocalizedModule T f

Defined in

Mathlib.Algebra.Module.LocalizedModule.Basic

Cited by

1 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleIsLocalizedModule