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Theorems · Theorem · commutative algebra

FractionalIdeal.map_id

∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
  (I : FractionalIdeal S P), FractionalIdeal.map (AlgHom.id R P) I = I
Defined in
Mathlib.RingTheory.FractionalIdeal.Operations
Cited by
3 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebra
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Around this declaration

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

FractionalIdeal.mapEquiv_refl · cited by 0FractionalIdeal.mapEquiv_…FractionalIdeal.map_symm_map · cited by 0FractionalIdeal.map_symm_…FractionalIdeal.map_map_symm · cited by 0FractionalIdeal.map_map_s…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraSubmonoid · cited by 3086SubmonoidFractionalIdeal · cited by 423FractionalIdealAlgHom.id · cited by 196AlgHom.idFractionalIdeal.coeToSubmodule · cited by 130FractionalIdeal.coeToSubm…FractionalIdeal.map · cited by 20FractionalIdeal.mapFractionalIdeal.coeToSubmodule_injective · cited by 19FractionalIdeal.coeToSubm…Submodule.map_id · cited by 14Submodule.map_idFractionalIdeal.map_idCITED BYCITES

Cites9

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

Cited by3

Results whose statement or proof uses this declaration.