Theorems · Theorem · commutative algebra

LocalizedModule.divBy_mul_by

∀ {R : Type u} [inst : CommSemiring R] {S : Submonoid R} {M : Type v} [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  (s : ↥S) (p : LocalizedModule S M),
  (LocalizedModule.divBy s) (((algebraMap R (Module.End R (LocalizedModule S M))) ↑s) p) = p

Defined in: Mathlib.Algebra.Module.LocalizedModule.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 46 from the axioms · uses propext, Quot.sound
Assumes: CommSemiring AddCommMonoid Module

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites21

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
LinearMapstatement · cited by 10,215
RingHomstatement · cited by 10,189
Algebra.algebraMapstatement · cited by 4,706
Submonoidstatement and proof · cited by 3,086
Module.Endstatement · cited by 774
LocalizedModulestatement and proof · cited by 154
LocalizedModule.mkproof · cited by 73

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.