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Theorems · Theorem · commutative algebra

LocalizedModule.mk_add_mk

∀ {R : Type u} [inst : CommSemiring R] {S : Submonoid R} {M : Type v} [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {m1 m2 : M} {s1 s2 : ↥S},
  LocalizedModule.mk m1 s1 + LocalizedModule.mk m2 s2 = LocalizedModule.mk (s2 • m1 + s1 • m2) (s1 * s2)
Defined in
Mathlib.Algebra.Module.LocalizedModule.Basic
Cited by
5 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringAddCommMonoidModule
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Around this declaration

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

IsLocalizedModule.mk'_add_mk' · cited by 2IsLocalizedModule.mk'_add…DivisibleHull.mk_add_mk · cited by 1DivisibleHull.mk_add_mkAlgebraicGeometry.StructureSheaf.const_add · cited by 0StructureSheaf.const_addLocalizedModule.lift'_add · cited by 0LocalizedModule.lift'_addIsLocalizedModule.fromLocalizedModule'_add · cited by 0IsLocalizedModule.fromLoc…Module · cited by 20661ModuleAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringSubmonoid · cited by 3086Submonoidmul_comm · cited by 2262mul_commLocalizedModule · cited by 154LocalizedModuleLocalizedModule.mk · cited by 73LocalizedModule.mkOreLocalization.oreDiv · cited by 72OreLocalization.oreDivOreLocalization.oreDiv_add_oreDiv · cited by 2OreLocalization.oreDiv_ad…LocalizedModule.mk_add_mkCITED BYCITES

Cites9

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