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Theorems · Theorem · commutative algebra

IsLocalization.coeSubmodule_mul

∀ {R : Type u_1} [inst : CommSemiring R] (S : Type u_2) [inst_1 : CommSemiring S] [inst_2 : Algebra R S]
  (I J : Ideal R),
  IsLocalization.coeSubmodule S (I * J) = IsLocalization.coeSubmodule S I * IsLocalization.coeSubmodule S J
Defined in
Mathlib.RingTheory.Localization.Submodule
Cited by
1 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringCommSemiringAlgebra
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Around this declaration

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

FractionalIdeal.coeIdeal_mul · cited by 13FractionalIdeal.coeIdeal_…Algebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringSubmodule · cited by 7192SubmoduleIdeal · cited by 4748IdealAlgebra.ofId · cited by 166Algebra.ofIdIsLocalization.coeSubmodule · cited by 30IsLocalization.coeSubmodu…Submodule.map_mul · cited by 3Submodule.map_mulIsLocalization.coeSubmodule_m…CITED BYCITES

Cites7

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Cited by1

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